2006 activity report - consorzio rfx 2006 activity report technical scientific committee 18 january...

2006 Activity Report

2006 Activity Report Technical Scientific Committee 18 January 2007

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CONTENTS

1. Introduction pag. 3

2 RFX-mod pag. 5

2a Systems performance and control developments

2b MHD physics and mode control

2c Transport and confinement

2d Edge phenomena

3 Theory and modeling studies pag. 37

3a Nature of the RFP dynamo

3b Active control of MHD modes

3c ITG mode study

3d Greenwald density limit

3e Pinch effect for chaotic transport

3f ORBIT update and transport in various regimes

3g Edge modeling

4 Collaboration to other experiments (RFP and Tokamak) pag. 44

4a Collaboration on MHD studies

4b Collaboration on transport studies

4c Collaboration on edge physics

5 Diagnostics pag. 50

5a Multichannel MOSS Spectrometer

5b DNBI

5c Improvement of the SXR tomographic system

5d Integrated System of Internal Sensors

6 ITER pag. 53

6a ITER Neutral Beam Injector

6b ITER diagnostics

6c ITER vertical displacement events and disruptions

6d ITER ICH Antenna

6e EU Superconducting Dipole


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7 Tokamak Engineering pag. 72

7a JET

7b FT3

7c JT-60-SA

8 Fusion Spin-offs pag. 81

8a Low power plasma source at atmospheric pressure

9 List of Collaborations pag. 82

9a Collaboration with other RFP laboratories

9b Collaborations with Tokamak laboratories

9c Collaborations on Theory

9d Other Collaborations

10 Education and information to the public pag. 83

11 List of Publications 2006 pag. 85


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1. Introduction

The program of Consorzio RFX for the year 2006 has been presented and discussed at the 17th

meeting of the RFX Technical-Scientific Committee on 8 November 2005.

The program has been approved by the Board of Directors of Consorzio RFX on 30 January

2006 and by the Steering Committee of the Euratom-ENEA Association on 20 January 2006.

The final approval of the program and of the relevant budget was given by the Consorzio

Partners on 5 May 2006.

The key objectives of the 2006 program were:

- “the exploitation of the new capabilities of the modified RFX to obtain important and

sound scientific results both in terms of confinement improvement and of active control

of MHD instabilities;

- to start giving a significant contribution to the ITER construction, with particular

reference to the Neutral Beam Injector.”

The planned experimental schedule included 36 weeks of operation and the main scientific

lines were: plasma performance optimization and active control of MHD modes.

Increase of plasma current to the MA range was planned as a fundamental step in the 2006

plan.

RFX operations ran smoothly during the whole year, confirming the excellent reliability of the

machine and of its power supplies, diagnostics, control and data acquisition system. A total of

166 experimental days have allowed producing 2.887 pulses, 2014 of them being useful for

plasma physics.

The main results are reported in Section 2; among them it is worthwhile to note the successful

operation with plasma current in the 1 MA range, owing to the much smoother plasma-wall

interaction offered by the new active MHD control system.

The saddle coil system also allowed to directly drag the internally resonant m=1 modes, so

keeping rotation for the whole pulse.

Higher current operation has also been associated with higher probability of occurrence of

beneficial Quasi-Single Helicity states.

The wide range of explored plasma regimes allowed us to analyze the scaling of the main

transport and confinement properties as a function of the basic plasma parameters. A

comparison has been possible with old RFX data, clearly demonstrating the improvements

obtained by the Virtual Shell operation; in particular, the central electron temperature now

increases nearly linearly with current, whereas it tended to saturate in RFX.

Section 3 of this report summarizes the main results of the theory and modeling studies, aimed

both to improve the understanding of basic properties of particle and energy transport, and to

support the search of optimum MHD control scenarios.

Collaborations with other fusion laboratories (Section 4) have been quantitatively reduced with

respect to previous years, but very significant results have been obtained, in particular on MST

and ASDEX UG.


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The main planned diagnostic developments have been postponed to the second part of the year,

due to the late budget approval; moreover, some technical difficulties prevented us from taking

advantage of the new diagnostic neutral beam injector; nevertheless, some important

improvements (Section 5) have been obtained in spectroscopy and tomography.

Section 6 reports about the second main task of the 2006 program: the RFX contribution to

ITER.

According to plans, almost all efforts have been dedicated to the design of the Neutral Beam

Injector and to the preparation for the construction of the relevant Test Facility in Padova.

Work has been performed under an EFDA contract, regularly closed in May; two further

contracts have been placed during the year. The various options, in particular those including

the SINGAP accelerator and the RF ion source, have been developed at the level of detailed

design studies, including thermomechanical, structural and electrostatic analysis. New

solutions have been proposed for the power supply system, validated by a feasibility

assessment in collaboration with industry.

All these activities on the NBI enforced the RFX leadership at the EU level; moreover, a

significant collaboration has been established with the Japanese partners.

During 2006, a significant amount of work has been also dedicated to design and construction

tasks for Tokamak machines (Section 7); among the results, it is worthwhile to mention the

design of the new JET Enhanced Radial Field Amplifier.

Finally, Section 8 illustrates a new spin-off of plasma research, Section 9 reports the list of

collaborations and Section 10 lists the educational activities, traditionally being a key

commitment of Consorzio RFX.


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Fig.2.1: Average magnetic field vertical component on the equatorial plane without (pulse 18871) and with (pulse 19496) feedback control in the presence of the same reference.

2 RFX-mod

2a Systems performance and control developments

2a.1 Control of plasma equilibrium In view of the exploitation of higher plasma current regimes, the action of the equilibrium

controller has been improved, in terms of control quality, robustness and reliability. In

particular, in order to optimize plasma startup and equilibrium control, a characterization of

the load assembly of RFX-mod was carried out. The high number of electromagnetic probes

mounted on the components of the load assembly allowed to analyze the response to a variation

of the magnetic field vertical component of the three toroidal conducting structures (vacuum

vessel, shell and mechanical structure), whose eddy currents affect the plasma equilibrium

magnetic configuration. The analysis led to the design and implementation of the feedback

control system of the magnetic field vertical component before gas ionization and allowed

meeting the requirement of an accurate control independently of the magnetizing winding

programming [Marchiori06a]. Fig. 2.1 illustrates the average vertical field component on the

equatorial plane achieved before the plasma rise with and without feedback control in pulses

19496 and 18871, respectively.

To minimize the plasma position steady-state error, the controller was completed with an

integral action that was successfully commissioned and routinely used in the successive

experimental campaigns. To increase robustness and reliability of the system, a set of activities

was carried out, including:

- Development of a dedicated protection system against vertical and radial overstresses on

the field shaping coils and of an independent back-up, real-time application to check and

limit overstresses, whose aim is to enhance the protection reliability;

- Implementation of controlled ramp-down of the references of the field shaping amplifiers in

case of protection request either generated internally or originating from the Machine Fast

Protection System (SGPR);

- Development of a protection to avoid

overdriving the field shaping power

amplifiers and windings in case of

failure of the input measurements;

- Development of a protection to prevent

a drastic reaction, such as Full Poloidal

Shutdown, in case of reversal failure;

- Limitation of voltage reference

derivatives to avoid voltage unbalance

on the field shaping power amplifiers,

resulting in a shutdown request;


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Fig. 2.2: Generation of m=1 n=-7 mode. Magnetic field spectra obtained without (yellow) and with decoupling (solid).

- Introduction of a dead-band for the plasma current where the control is inactive, in order

to avoid intervention of the system in the first period of the discharge, where the shell

passive action is predominant.

Some minor issues concerning equilibrium control still remain open, such as, for instance,

filtering of the currents to avoid ripple propagation to the references and the development of a

non-linear, anti-windup scheme to avoid excessive control delay due to the integral action.

2a.2 Control of MHD modes A significant effort was devoted in 2006 to the development and validation of models for MHD

mode control and in their experimental testing.

First of all, an electromagnetic model of the active system was developed, taking into account

the toroidal geometry and the effects of passive structures. The model parameters were

estimated by processing experimental data collected in dedicated measurement campaigns.

State space representations were adopted to describe the dynamics of the active saddle coil

currents and the fluxes measured by saddle probes. Open and closed loop responses were

computed and compared with experimental data. Through this model a static matrix M was

obtained accounting for the mutual coupling among saddle coils and among saddle coils and

sensors [Marchiori06b]. Fig. 2.2 shows, as an example, by yellow bars the measured normalized

amplitudes of magnetic field modes when the system is used to generate in closed loop only the

m=1 n=-7 mode. In mode generation, no decoupling is used among coils. In this case, due to

toroidal geometry, the achieved magnetic

field spectrum shows the presence of two

spurious modes, the m=0 n=7 and m=2 n=7

ones, with noticeable amplitudes. The

spectrum is displayed in solid bars when the

generation is performed using the decoupling

block. As shown in the figure, the achieved

spurious mode suppression is very effective.

An m=0 n=7 component arises in the current

spectrum when using the decoupling block to

cancel the m=0 n=7 radial field mode. A

further tuning of the model was carried out

to improve its accuracy in reproducing the

magnetic field diffusion into the load assembly.

Significant work was also devoted to the optimization of the Virtual Shell (VS) control scheme. The power amplifiers and saddle coils were commissioned up to nominal current (400 A) and

control was applied routinely to achieve stabilization of resistive wall modes (RWMs), to induce

reproducible plasma rotation and to cancel the resistive kink tearing modes (TMs) at the sensor

radius [Bolzonella06].


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Fig. 2.3: Feedback control on RWMs. Comparison among pulses programmed with same parameters, but differing in RWM control.

Fig. 2.4:Power consumption associated to MHD mode control.

TM activity appears also reduced in the plasma core, as confirmed by magnetic measurements

and SXR double filter diagnostics. TM rotation was routinely achieved byapplying the VS

scheme, significantly contributing to the

alleviation of plasma wall interaction and

allowing, so far, the increase of plasma

current up to 1MA. Experimental

campaigns are in progress to reach full

design performances. The control of the

radial field boundary allowed executing

well controlled plasma pulses up to 360

ms, corresponding to six shell time

constants, far beyond the original design

value of 250 ms. Fig. 2.3 illustrates the

flexibility achieved in the cooperation of

the MHD mode control, comparing three

pulses programmed with the same parameters (the m=1 n=-6 being the most unstable RWM),

but differing in how RWMs are controlled.

Pulse #17301 (blue) is executed excluding

m=1 n=-6 to n=-3 RWMs from control.

The m=1 n=-6 unstable mode grows and

when its amplitude reaches a few mT the

pulse is early terminated. Pulse #17287

(red) is executed with full VS control

(except, as usually, for the m=1 n=0

equilibrium field). The amplitude of the

m=1 n=-6 mode is kept at negligible

values and the plasma current is well

sustained up to 250 ms. Pulse #17304

(green) is executed letting the m=1 n=-3

to n=-6 free to grow until t=150ms and at

this point control is applied on the modes

so promptly reducing mode amplitude (in

~10ms) to very low values.

To quantify the power needed in RFX-

mod for mode control, fig. 2.4 shows the

power supplied by the power amplifiers to

control the MHD modes by means of VS

in pulse #19648 at 1 MA. In this pulse the references for the m=1 n=-7, -8, -10, -11, -12 TM are

not preset to cancel the modes, but to produce rotating modes. The figure shows, from top to


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Fig. 2.6: Simulation of system response in terms of toroidal field at the wall.

Fig. 2.5: Block diagram of Mode Control.

bottom, the plasma current, the power

supplied by the amplifiers for MHD mode

control, the ohmic power associated with the

plasma, and the m=1 spectrum at flat-top,

respectively. During the flat-top the power

needed to control the MHD mode is ~1% of

the plasma ohmic power [Luchetta06].

Another important task was the

development of advanced control schemes,

such as the Closer Virtual Shell and the Mode Control with and without sideband suppression.

The Closer Virtual Shell algorithm computes the field distribution in the region between the plasma and the sensors and aims at creating a VS beyond the sensor radius. This technique, currently being experimented, can force the magnetic boundary at any radius in the vacuum region between the last closed flux surface and the active coils.

Direct Mode Control was implemented introducing a derivative control to compensate for the radial field penetration delay due to the passive structure. As the delay depends on the mode

number, it was not straightforward to model the compensation in the VS. Fig. 2.5 displays the

block diagram of MC. The main difference with VS is that the regulators act directly on the harmonic components. To smooth the derivative action, a filter (1-pole Butterworth) is applied

to the mode components.

Attention was also paid to sideband suppression, as the discrete coil system intrinsically

produces magnetic field sidebands at

the sensors. These spurious

components add to the mode signals

and are seen by the control system as

spatial aliasing. A model was

developed and implemented to

compute the sidebands and to clean

the vertical field mode signals. The

development and the optimization of

these advanced control schemes is

still ongoing and will continue during

2007.

2a.3 Control of Toroidal field The toroidal power amplifiers and


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windings were commissioned up to 12 and 5 kA of direct and reverse currents, respectively.

Various control schemes were developed and tested, among which the control of m = 0 modes

and the feedforward control of the reversal parameter F and of the safety factor q at the edge. A

new feedback control system of the toroidal field at the wall was also designed on the basis of a

dynamic model which accounts for the closed loop response of the toroidal winding current

during the flat-top and the perturbation due the vessel poloidal current. In figure 2.6 a

simulation of the system response in terms of toroidal field at the wall and inverter current

reference is shown in the case of a field reference step variation. The desired value is achieved

within 20 ms, while the limit inverter current reference is reached for a very short time. The

system capability to compensate for field perturbations due to poloidal loop voltage variations

is also shown in the simulation. The effect of 2 V step variation of the poloidal loop voltage is

cancelled again within 20 ms.

An extension to the feedback control of F was studied in view of more advanced operation

scenarios in which simultaneous control of F and Theta parameters could be implemented. The

commissioning and experimental tests of this new system are expected in the next months.

2b MHD physics and mode control

Following the highly successful initial Virtual Shell (VS) experiments of 2005, active MHD

control studies continued also in 2006 on RFX-mod. On the one hand very effective rotation

schemes were developed, which allowed safe and successful extension of the plasma current

range up to 1.1 MA. On the other hand, several advanced RFP scenarios were also studied in

more detail. QHS studies entailed both the analysis of the “spontaneous” and “stimulated”

state transitions, Oscillating Poloidal Current Drive (OPCD) experiments were extended up to

1MA, Self-Similar Current Decay (SSCD) scenarios were explored in more detail. Studies on

Oscillating Field Current Drive (OFCD) and RWM control continued and will also be briefly

outlined in the following sections.

2b.1 Mode rotation and 1MA pulses In RFX the lack of control of radial fields at the plasma boundary hindered operation at high

current. Nearly 50% of pulses at Ip > 0.9 MA suffered “fast” terminations and most of the

remaining ones showed carbon blooms due to highly localized Plasma Wall Interaction (PWI)

[Bartiromo00]. In those conditions some relief was found by Oscillating Poloidal Current Drive

(OPCD) [Bolzonella01] or rotating the locked mode (LM) by Rotating Toroidal Field Modulation

(RTFM) [Bartiromo99].


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Conversely, the improved materials and magnetic boundary of RFX-mod VS [Zanca06a,

Paccagnella06] allow performing long and well controlled 1 MA pulses [Ortolani06], where the

on axis loop voltage is in the range 20÷30 V, compared to the 30÷50 V of RFX pulses at the

same current (Fig. 2.7). The temperature and the confinement time are also higher with a

positive current scaling, which, contrary to the past, does not show any saturation at 1 MA

[Innocente06], leading to τE ∼1.5 ms. Nonetheless, the incomplete field error correction by the

saddle coils still causes the PWI to concentrate in the region of the LM. This results in a rapid

deterioration of the wall conditioning, which

calls for frequent sessions of H and He GDC.

A solution to this problem is to spread power

deposition around the torus by externally

inducing the rotation of the MHD modes. To

this end, RTFM can be used also in RFX-mod.

The LM is rotated around the torus at 10÷20

Hz by applying an m = 0 n = 1 mode of a few

mT in terms of Br(a). Unfortunately, although

such values are lower than those needed in the

past, in RFX-mod with VS they cause an

increase of a few volts of the loop voltage. This is explained by considering that the largest

residual deformation of the edge magnetic surface with VS is due to the m = 0 component

[Martini06]. Hence, even the small additional error due to RTFM gives a non-negligible

contribution to localized PWI.

On the other hand, we developed several new schemes for the rotation of internally resonant m

= 1 modes by rotating m = 1 perturbations applied via

the saddle coils. They take advantage of the direct

coupling of each perturbation with the homologous

mode, which occurs at the corresponding resonant

surface. We used both Mode Control (MC) with complex

gains and VS + rotating perturbation schemes

[Luchetta06]. The MC + complex gains applies a

spatially out-of-phase correction to each mode, thus

applying a torque that can be increased by increasing

(in modulus) the phase of the complex gain. Of course

the larger is such a phase, the higher is the residual

field error, because of the incomplete correction. The

scheme results in a rotation frequency of the order of

10÷20 Hz. In the VS + rotating perturbation schemes

the applied torque on each mode is proportional to the

toroidal angle (deg)

polo

idal

ang

le (d

eg)

18840

0

60

120

180

240

300

360

0 60 120 180 240 300 360

18741

0

60

120

180

240

300

360

toroidal angle (deg)

polo

idal

ang

le (d

eg)

18840

0

60

120

180

240

300

360

0 60 120 180 240 300 360

18741

0

60

120

180

240

300

360

Fig. 2.8: Footprint of LM maxima with active rotation: with MC + complex gains (top); with VS + rotating perturbations (bottom, path of an m=1 n=7 mode in red).

10

20

30

40

50

60

70

80

0 5 10 15

RFX

RFX-mod

Power (RFX)

Power (RFX-mod)

Vφ (0) [V]

I/N·10-14 (Am)10

20

30

40

50

60

70

80

0 5 10 15

RFX

RFX-mod

Power (RFX)

Power (RFX-mod)

Vφ (0) [V]

I/N·10-14 (Am)Fig. 2.7: On axis toroidal loop voltage vs I/N in RFX and RFX-mod pulses at ≈ 1 MA


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applied perturbation. We found that a Br(a) perturbation smaller than 0.5 mT, i.e. comparable

to the VS residual error, is adequate for mode

rotation at frequency up to 40 Hz.

Both techniques are very effective, with some

important differences. The complex gains

scheme works with somewhat smaller field

errors at the expense of a rotation velocity

which “adjusts” itself to the plasma conditions.

The latter feature is a drawback for LM

rotation at high current. In fact when the

complex gain is applied to several modes,

because of their non-linear coupling, they all

rotate at the same frequency. This results in a

“poloidal rotation” of the LM (Fig. 2.8), which

does not accomplish the desired toroidal

spreading of the localized power load.

A more effective LM rotation is obtained via

the VS + rotating perturbations schemes,

which allow controlling the mode-mode relative

phases.

The best results are obtained rotating

several modes with frequencies equally-

spaced according to their n-number (e.g. n=-8

at 10 Hz, -9 at 20 Hz, -10 at 30 Hz and so on).

The initial phase of each mode is set equal to

the one present in the plasma (computed in

real-time). In this way the modes are hooked

up in the shortest possible time, their

relative phases are maintained and the

interference pattern of the LM is helically

dragged along the path of a stationary m=1

mode (n= -7 in the case of Fig.2.8). Moreover,

thanks to the combined non-linear coupling, the m=1 modes apply a rotating torque on the m=0

n=1 mode, which responds with occasional large toroidal “jumps” not normally seen in standard

VS pulses.

The effectiveness of such LM rotation scheme is highlighted in Fig. 2.9, where 8 pulses with

plasma current larger than 1 MA and lasting over 0.35 s are superimposed. As a result of a

steady LM rotation, density control is maintained pulse after pulse and plasma performance is

0

100

200

300

400

500

600

700

800

-0,5 -0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5

ensemble av. 1 MAfit 1MA19531 OPCD t=0,095 s

Te (eV)

r (m)Fig.2.10: Te profile at 1 MA with VS + rotating perturbation (ensemble average of Fig.2.9 pulses) and with OPCD (pulse 19531)

0200400600800

10001200

0 0,1 0,2 0,3 0,4

0

1020

30

4050

0 0,1 0,2 0,3 0,4

0

1

2

3

4

0 0,1 0,2 0,3 0,4

0100200300400500600

0 0,1 0,2 0,3 0,4

-1200

-700

-200

300

800

0 0,1 0,2 0,3 0,4

1967619669196781969919700197011970219761φ

LM (d

eg)

Τe (e

V)

n e ·1

019(m

-3)

Vφ(V

)Ι p

(kA

)

Start of controlled run down

a

b

c

d

e

t (s)

0200400600800

10001200

0 0,1 0,2 0,3 0,4

0

1020

30

4050

0 0,1 0,2 0,3 0,4

0

1

2

3

4

0 0,1 0,2 0,3 0,4

0100200300400500600

0 0,1 0,2 0,3 0,4

-1200

-700

-200

300

800

0 0,1 0,2 0,3 0,4

1967619669196781969919700197011970219761φ

LM (d

eg)

Τe (e

V)

n e ·1

019(m

-3)

Vφ(V

)Ι p

(kA

)

Start of controlled run down

a

b

c

d

e

t (s)Fig. 2.9: Superposition of 8 VS + rotating perturbation 1 MA pulses: a) plasma current; b) loop voltage; c) line average ne; d) central Te; e) LM toroidal angle.


- 12 -

very reproducible both in terms of plasma current, loop voltage, electron density and

temperature. The Te profiles are also very similar and broad (Fig. 2.10) with central values of

400 eV.

2b.2 QSH states 2b.2.1 Spontaneous QSH studies

The new magnetic feedback system available in RFX-mod has radically influenced the MHD

phenomenology with respect to what previously studied in RFX. This had significant effects

also on the transition to Quasi-Single Helicity (QSH) states, both in terms of reproducibility

and performance.

In particular, the Virtual Shell (VS) control

scheme has been proved to be highly beneficial

for the spontaneous transition to QSH

[Piovesan06]. The smoother magnetic boundary

obtained with VS operation allows to reach

purer and more frequent QSH spectra, generally

characterized by improved duration and thermal

energy content. Such transitions to QSH exhibit

either a quasi-stationary or an intermittent

dynamics. The intermittent, sawtooth-like

dynamics, typical for example of the MST

discharges, is observed for the first time in RFX-

mod and only during VS operation.

The dynamics and duration of the QSH states in

the VS scenario is clearly correlated with plasma parameters like plasma current and magnetic

equilibrium. In particular high-current operation tends to favour longer, quasi-stationary QSH

states, as shown in Fig. 2.11. High plasma current also increases the QSH transition

probability. These observations are very promising for the next future experiments in RFX-mod

at plasma currents towards 2MA.

The soft x-ray (SXR) tomographic diagnostic installed in the RFX-mod device [Franz01] allows

characterizing the SXR emissivity with high spatial resolution (78 lines of sight spanning an

entire poloidal cross-section) and with a frequency bandwidth of several kHz. The 2D

emissivity maps obtained with tomographic algorithms permit to study in detail the plasma

dynamics in different operational scenarios. In particular, a highly emissive island region is

observed in the plasma core during QSH states, which corresponds to the helical flux surfaces

associated with the dominant mode in the magnetic spectrum.

Fig.2.11: QSH duration as a function of QSH probability for a large database of RFX-mod Virtual-Shell discharges at different plasma current.


- 13 -

Similar structures are also observed during mode control experiments. In these cases the

reconstructed emissivity is an important tool for determining whether the imposed rotation of

the magnetic field at the edge is

followed by rotation of the mode inside

the plasma. Such a correspondence is

shown in Fig. 2.12. Here the poloidal

position of the island computed from

edge magnetic and internal SXR

measurements are compared and a

good match is found confirming that

the external action has a

corresponding effect in the plasma

core.

Internal reconstructions of the

magnetic flux surfaces based on soft x-

ray tomography, Thomson scattering

and ORBIT modelling have also shown

that a helical core with good confinement properties is sometimes

associated also with magnetic spectra

being apparently in the Multiple

Helicity state, based on external magnetic measurements. This is explained by the fact that the

resonant radius of the m=1,n=-7 mode, which dominates the spectrum during QSH, is very

close to the magnetic axis, in a region with low magnetic shear.

The availability of a higher spatial resolution (7mm) Thomson scattering diagnostic allows to

characterize with high detail the electron temperature profiles during QSH states. Moreover,

when the diagnostic is absolutely calibrated, also the electron density profile can be measured,

with enough accuracy to open new perspectives in the study of thermal islands. In particular

the Thomson scattering diagnostic has shown that the intermittent QSH states are associated

with the most reduced core heat diffusivity. In fact, as will be shown even clearer in Sect. 2c.4,

a further tenfold reduction of the electron heat diffusivity, which reaches values χe≈100m2s, is

measured in the QSH island region. As expected from this analysis, also the electron energy

confinement time is enhanced accordingly up to 0.8ms [Innocente06].

An increased QSH probability transition is registered during inductive profile control through

oscillating poloidal or oscillating field current drive (OPCD and OFCD) techniques. These QSH

plasmas are characterized by even further improved confinement characteristics: the island

radial width increases up to 25cm, the electron temperature inside the island reaches values of

700eV, with a radial gradient comparable to the edge gradient.

Fig. 2.12: Angular position of the magnetic island and of the center of mass of the SXR emissivity: the magnetic phase rotation is externally induced in a VS scenario. The SXR reconstructions at two different instants confirm the island rotation at the tomography section.


- 14 -

These same island structures are also observed by the SXR diagnostic, which allows following

in time their dynamics. In the OPCD anti-dynamo phase, the MH state is mainly re-

established, even if sometimes a residual structure is maintained, due to the residual radial

component of the dominant magnetic mode: the high spatial resolution of the SXR tomography

allows reconstructing the SXR asymmetries associated to the residual component of the

magnetic island.

In the OPCD scenario, the 2-D reconstructed maps have been also compared with the signals

from the new multifoil diagnostic [Bonomo06] to estimate electron temperature profiles over

the low field side of the RFX-mod chamber. In correspondence to the localized SXR structures,

the electron temperature profiles show an evident asymmetry (see Fig. 2.13) similar to the

Thomson scattering measurement, with the SXR structures being characterized by a higher

temperature than the plasma nearby. Further analysis will be done in order to characterize

also with this diagnostic the temperature inside the islands.

2b.2.2 Active control of internal resistive MHD modes

The flexibility of the new MHD controlsystem allows specifying different feedback laws for the

various helicities (Selective Virtual Shell, SVS). This flexibility has been used to perform

experiments [Marrelli06] aimed at studying the effect of different boundary conditions on the

dominant resonant modes (m = 1, n = -7, -8, -9, -10) and in particular at investigating the

possibility of stimulating the onset of Quasi Single Helicity spectra. Experiments have been

performed on 600 kA and 800 kA discharge. In Selective Virtual Shell the radial field of every

harmonics resolved by the sensor coils can be independently controlled: in particular, in a first

set of experiments (“natural evolution”) control on selected helicities has been inhibited; other

experiments have been performed by assigning a non zero reference value for selected

helicities.

In natural evolution experiments, for helicities m = 1; n = -7,…, n = -10, corresponding to the

most unstable tearing modes, both the toroidal and the radial component of the field grow.

Similarly to what happens in spontaneous transition to QSH, the increase of the dominant

Fig 2.13 (a) Electron temperature (Te) profile from the new multifoil diagnostic (p is the impact parameter): the localized Te increase in the plasma core is due to the presence of a more emissive SXR structure emerging in the plasma core, as illustrated in (b).

(a) (b)


- 15 -

mode occurs simultaneously with a decrease of secondary modes. The drawback of this

technique is that discharge duration is systematically shorter than the reference one, as the

increase of the radial component implies a considerable non axisymmetric shift of the last

plasma surface. In “non-zero reference value” experiments, the amplitude and phase of the

radial component of a selected mode has been feedback controlled: values up to 3-4 mT have

been tested. In this scenario the discharge duration is comparable to reference SVS discharges.

The measured amplitudes of the harmonics reproducibly follow the reference value with a time

delay of the order of 5-10ms: the feedback system compensates, in fact, the different wall

penetration time of the various harmonics. When the plasma is present, the harmonics of the

applied field (obtained from the measured currents flowing into the control coils by a dynamic

model that takes into account the mutual inductances between saddle and sensor coils

[Marchiori06b]) are out of phase compared to the measured radial field harmonics: as long as

the reference value of the field is below the value it would reach without control, the externally

applied field is opposed to the one produced by the plasma. An example is shown in Fig. 2.14,

where the non-zero reference value for mode n = -7 started before discharge breakdown. In the

first phase, when no plasma is present (t < 0), the model reconstructed applied field coincide

with the measurement (both in amplitude and phase): i.e. the field is produced by the saddle

coils only. When the plasma is present (t > 0), the phase of the control harmonic switches to π

in order to apply a field opposed to the plasma generated one.

The radial component amplitude and phase can be well

controlled: in particular the phase of the plasma mode

(both radial and toroidal components) follows the

reference phase, and SXR islands locations are aligned

with the magnetic islands O-point. Given the evidence

that the phase of the plasma mode can be controlled, in a

subsequent set of experiments, the reference phase of a

selected mode was linearly varied in time. It is found

that rotations of the m = 1, n = -7 phase up to 20Hz can

be obtained. Both the radial and the toroidal component

phases rotate and intermittent SXR structures

(indicating the presence of a core helical structure) are

observed, when the magnetic spectrum displays a

transition to a QSH state. In particular, for the first time

in RFX, the thermal structures appeared at different

poloidal locations for different times in the same

discharge.

0 50 100 150 200 250 3000.00.51.01.52.02.5

b r-7

(m

T)

ReferenceMeasuredExternally applied

a)

# 17511

0 50 100 150 200 250 300

-3

-2

-1

0

phas

e (r

ad)

b)

0 50 100 150 200 250 300t (ms)

0123456

b φ(m

T)

n= -7n= -8n= -9n= -10

c)

Fig. 2.14: Time evolution of the (1,-7)mode. a) amplitude, b) phase for reference, measured and external field. c) Toroidal harmonics for the same shot.


- 16 -

2b.3 Oscillating Polidal Current Drive experiments OPCD had been first tested on RFX [Bolzonella01]. It proved the possibility of improving

plasma confinement in steady state (oscillating) by the reduction of dynamo modes via

inductive poloidal current drive. In RFX it showed a positive scaling with plasma current and a

contribution to the improvement of plasma performance was also given by the periodic

mitigation of localized PWI. The latter effect is less important in RFX-mod with VS, because of

the improved magnetic boundary, therefore the confinement increase is not very large at low

currents. Conversely, a recent set of experiments at 1MA shows that OPCD in conjunction with

VS sistematically induces QSH states by reducing the amplitude of secondary dynamo modes.

Such reduction of secondary modes was clearly identified as the underlying cause for

confinement improvements resulting in central Te increases of 30%, with the onset of a temperature

gradient also in the plasma core (Fig. 2.10 e 2.15).

Detailed analyses of OPCD experiments highlighted

several interesting features, such as the decrease of

magnetic and density fluctuations during the co-

dynamo phase: another signature of the transport

improvement obtained with this technique.

2b.4 Self-Similar Current Decay experiments The Self-Similar Current Decay (SSCD) has been suggested as an interesting operation mode

for the RFP. The concept is that the dynamo should be “switched off” when the magnetic field is

forced to decay with suitable rate at fixed radial profile.

Numerical simulations predict a decrease of mode

amplitude and stochasticity. More experimental test of

SSCD have been performed in RFX-mod in 2006

[Zanca06b]. A regime, characterized by transient states

close to the m=1, n=-7 single helicity, establishes. The

magnetic regime induced by SSCD results in a 50÷100%

increase of the energy confinement time, as shown in Fig.

2.16.

2b.5 Oscillating Field Current Drive experiments The OFCD technique aims at stimulating a plasma response by oscillating poloidal and

toroidal magnetic fields at the plasma surface. Due to the plasma non linear response to these

oscillations, OFCD actively interacts with the RFP dynamo mechanism and this can result in

net drive of toroidal plasma current. In this way, OFCD can add the perspective of non

inductive current drive to the beneficial effects on confinement of pure OPCD operations.

0

0,5

1

1,5

2

2,5

3

50 60 70 80

τE

SSCDstart

t (ms)0

0,5

1

1,5

2

2,5

3

50 60 70 80

τE

SSCDstart

t (ms)Fig. 2.16: τΕ during SSCD at 600 kA (ensemble average).

Fig. 2.15: Te profile at maximum co-dynamo (red) and counter-dynamo (blue) OPCD cycle.


- 17 -

The first task of 2006 OFCD operation was the integration of the technique with full virtual

shell operation. This allowed the application of OFCD to Ip≈0.8 MA plasma discharges of ≈250

ms duration and more than 100 ms of well-controlled flat-top. Having long discharges is a key

issue, since it allows summing the effect of many cycles of operation. On this kind of plasmas

the present capabilities of the toroidal and poloidal power supply systems were tested in terms

of attainable amplitudes, frequencies and relative phasing.

As an example, in Fig. 2.17 the result of a set of 100 Hz experiments is shown: keeping

constant the timing of the toroidal field oscillations (poloidal loop voltage, third frame), the

initial phase of the magnetising system (toroidal loop voltage, second frame) is changed. The

resulting toroidal flux (first frame) is then analysed for the different relative phasing. It is

interesting also to note how the resulting amplitude of the toroidal loop voltage oscillations at

the plasma edge changes with phase as a result of the interaction between the two systems,

despite the same oscillating amplitude is pre-programmed on the toroidal and poloidal coils.

First tests of periodical non-sinusoidal oscillations (e.g. square or sawtooth-like waves) were

also performed, with the aim of studying the effect of many harmonics penetrating with

different characteristic times. Further developments of OFCD will be pursued in 2007.

2b.6 Stabilization of RWMs Studies on Resistive Wall Mode (RWM) physics and their active control continued in 2006 with

particular attention to the characterisation of the instability spectra for different plasma

equilibria (i.e. for different values of the reversal parameter F), and to the study of new control

techniques, especially those of common interest for RFP and tokamak configurations.

Fig. 2.17: Example of phase scan for oscillations of about ± 12 V in the toroidal loop voltage (second window) and 6 V in the poloidal loop voltage (third window) for 100 Hz experiments. Resulting toroidal flux is shown in the first window. Black (18904): reference; red (18931): δ≈0; blue (18937): δ ≈π/4; cyan (18939): δ ≈-π/2; grey (18912): δ ≈π/2.


- 18 -

Part of the first point was also the study of the plasma response to pre-programmed field

errors, the so-called resonant field amplification or RFA. This subject is particularly important

since it allows studying the effect of small, but unavoidable, magnetic field inhomogeneities on

RWM destabilisation. The flexibility of the new active control system allowed the creation of

static and rotating error fields with different amplitude and phase, and the characterisation of

stable, unstable and metastable (or marginally stable) modes for different plasma equlibria.

The RFA experiments have been carried

out in collaboration with the MPG-IPP

group in Garching (Germany). The

effectiveness of the control system on

events happening in the middle of a

plasma discharge can be tested in

experiments like the one presented in

figure 2.18. One unstable RWM is on

purpose not controlled between t=80 ms

and t=150 ms reaching in this way a

small amplitude (0.5 mT for the

experiment shown). After t=150 ms the

control on the RWM is turned on again

and in a very short time (∆t


- 19 -

pick-up coils is filtered (25 point median

algorithm); the output is able to cancel the

slow m=0 dynamics: the actuators in fact are

the 12 sectors of the toroidal power supply. In

this type of experiments, the m=0 control has

been added to a standard, Virtual Shell

discharge. Results are encouraging: the total

m=0 Bt fluctuation amplitude has been

decreased (Fig. 2.19), and indications of a

decreased plasma-wall interaction have been

obtained. In fact, it seems that the control of

the m=0 modes is crucial in the startup phase of the

discharge, when the toroidal Bt field is reversed, and

the plasma-wall interaction is larger.

2b.8 Reversed Field Tokamak The underlying idea of the Reversed Field Tokamak

(RFT) operation is to first form a quasi-stationary

tokamak, and then make the transition to a RFP by

raising the loop voltage and reversing the toroidal field

at the wall. The foreseen advantage would be to start

from a relatively hot tokamak plasma, thus possibly

obtaining a better RFP state. Transiently, a new

configuration with on axis q ~1 and reversed edge q

should be formed.

During 2006, the completion of the commissioning of

the toroidal field system brought the available

maximum toroidal field up to 0.5 T. Therefore, the

formation of a tokamak-like plasma, with low loop

voltage (~ 3 V) and plasma current IΦ of about 80 kA,

which corresponds to q(a)∼3, was successfully

achieved (Fig. 2.20), using only the flat top power

supplies for all the discharge phases (including

breakdown). During the almost stationary tokamak

phase of the discharges the growth of a low

frequency instability, typically characterized by m=3

mode number, has been observed by analysing the

magnetic signals of the ISIS system (Fig.2.21), and

also fast intense magnetic activity, associated to negative spikes in the loop voltage.

Fig. 2.19: Example of feedback control of m=0 modes: in the controlled discharge, the total fluctuation amplitude of the m=0 modes is reduced (blue line) with respect to the standard, Virtual Shell discharge (red line).

Fig. 2.21: Spectrogram of a Br signal from the ISIS system, showing the development of a m=3 mode.

Fig. 2.20: Typical plasma current IΦ, loop voltage Vt(a) and q(a) signals for a RFT discharge. The attempt of transition from the tokamak to the RFP configuration starts at about 60 ms, in this case (shot #20737).


- 20 -

In the first attempts of transition to the RFP, a reversed configuration was not obtained, but a

minimum q(a) close to 0.3 has been reached, without suffering major disruptions during the

development of the m/n=1/1 kink mode in correspondence of a q(a)=1 condition. A preliminary

scan on different relative temporizations, between the increase of the plasma current and the

decrease of the toroidal magnetic field at the wall, has shown that this is a crucial aspect in

order to reach a final RFP configuration, along with the achievement of a correct feedback

control of the horizontal shift by means of the

vertical field coils system.

2c Transport and confinement

To study confinement properties, a large

database has been realised using all RFX and

RFX-mod shots. To improve the analysis, kinetic

quantities have been included in the database

only if measured with small errors and profile

measurements have been used where possible.

Electron temperature profiles are computed by

fitting Thomson Scattering multipoint

measurements [Alfier06b] by a two-parameter

temperature profile Te(r)=Teo(1-rα). Electron density profiles are computed by inverting the multi-chord interferometer measurements. To account for hollow density profiles, we use a four

parameter density profile ne(r)=neo-(neo-ne1-nea)rα-ne1rβ [Gregoratto98]. Ion temperature was deduced by Doppler broadening of OVII lines when available.

Poloidal beta (βp) (which in RFPs is about 50% higher than the volume average beta) and

energy confinement time (τE) are computed by integrating temperature and electron density

profiles. To increase the number of data-points the confinement analysis has been performed

assuming Ti=Te because after wall boronization the OVII line emission is blended with Boron

lines and the measurements of Ti became very uncertain. The Ti=Te assumption has been

verified by comparing Ti with Te, when both are available. Fig. 2.22 shows that the two

temperatures are approximately equal, with higher Ti at lower temperature and lower at

higher temperature. The assumption Ti=Te is hence justified at intermediate temperatures

while it is conservative at low T. On the other hand, at high temperatures Ti measurements are

affected from uncertainty in evaluating the OVII radial position, which gives a systematic

underestimation of Ti. The measurements of Ti with a neutral beam, recently installed on

RFX-mod, will allow more precise evaluations in the near future.

100

150

200

250

300

100 150 200 250 300

RFX-mod VS

T i(0

) (eV

)

Te(0) (eV)

Fig. 2.22: Central ion temperature versus central electron temperature.


- 21 -

The experiments explored a large range in most of

the operational parameters, with plasma current in

the range Ip=0.1÷1 MA and density in the range

ne=0.5÷6·1019 m-3. In Fig. 2.23 Ip/N (N=πa2 is the line density) and q(a) obtained at the different

plasma currents Ip are shown for three RFX

operation modes: RFX, RFX-mod NVS and RFX-

mod VS. The figure shows that RFX-mod operates

typically at a higher Ip/N parameter than the old

RFX, in particular at currents over 800 kA the

highest Ip/N are only obtained by RFX-mod. Finally,

in RFX-mod currents over 600 kA are only explored

in VS mode, to avoid first wall damage.

2c.1 Confinement properties The values of βp and τE obtained for the three RFX

experimental conditions are drawn in Fig. 2.24.

Figure 2.24a shows that βp varies from 2% to 15%,

it is similar for both RFX-mod operation modes and is slightly higher than that of the thick

shell RFX. Finally, it clearly depends on the Ip/N parameter. Figure 2.24b shows that τE can

reach values up to 1.5 ms in RFX-mod, it is on average 50% higher for the VS operation

compared to RFX and about twice than the RFX-mod NVS operation. Energy confinement time

of RFX-mod steadily increases with plasma current while in RFX it showed a maximum at

about 600÷800 kA.

A quantitative comparison of the performance in the three experimental conditions is obtained

by averaging βp and τE of stationary discharges (low dIp/dt) in a small parameter range.

Selecting the interval Ip=550÷600 kA, Ip/N=3.5÷4.0⋅10-14 Am and F=-0.25÷-0.05, we obtained

0

5

10

15RFX-mod VSRFX-mod NVSRFX

I p/N

(Am

*10-

14)

-0.1

-0.08

-0.06

-0.04

-0.02

0

0 200 400 600 800 1000

q(a)

Ip (kA)

Fig. 2.23: Operational range in the (Ip,I/N) and (Ip,q(a)) parameters for RFX, RFX-mod standard operation (NVS) and RFX-mod with

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 200 400 600 800 1000

RFX-mod VSRFX-mod NVSRFX

τ E (m

s)

Ip (kA)

(b)

0

2

4

6

8

10

12

14

0 5 10 15

RFX-mod VSRFX-mod NVSRFX

β p (%

)

Ip/N (Am*10-14)

(a)

Fig. 2.24: Poloidal beta and energy confinement time for the three RFX experimental conditions.


- 22 -

=3.4 %, NVS=4 % and VS=4.6 % for poloidal beta and =0.58 ms, NVS=0.36

ms VS=0.80 ms for energy confinement time. At higher currents, where only RFX and

RFX-mod VS data are available, τE is twice for RFX-mod compared to RFX.

2c.2 Scaling laws To better understand the phenomena underlying confinement, we have studied the dependence of βp and τE on the main plasma parameters for RFX and RFX-mod VS.

Poloidal beta shows the clearest scaling: all the VS data of stationary discharges can be fitted

by a single parameter exponential fit βp ∝ (Ip/N)-0.74 (regression coefficient R=0.9). The RFX thick shell discharges are better described by a two parameter fit βp∝Ip-0.46(Ip/N)-0.50 (multiple regression coefficient R=0.7). The additional negative dependence on plasma current obtained

in RFX is similar to that obtained in T2 experiment and to the βp∝Ip-0.56(Ip/N)-0.56 predicted by 3-D resistive MHD simulations performed by the

DEBSP code [Brunsell00]. The result of RFX-

mod VS, where the addition of the Ip as

independent parameter is not necessary in order

to have a good scaling, shows that by lowering

edge error fields (and then by controlling the

plasma-wall interaction), it is possible to obtain

the same βp at higher plasma current for a given

I/N.

Energy confinement time shows a less clear

dependence on the main plasma parameters. In

the RFX-mod VS case a two parameter fit

provides a relatively good regression

τE∝Ip0.72(Ip/N)-0.23 (multiple R=0.68), while a much worse (multiple R=0.3) regression τE∝Ip0.40(Ip/N)-0.16 is obtained in RFX, showing that other hidden parameters affect RFX results. A better scaling law is obtained for the VS data by a three parameter fit, using Ip, Ip/N and b8-15, the sum of the amplitudes of the toroidal field modes with m=1 and n=-15÷-8. The least

square fit of τE is drawn in Fig. 2.25. The goodness-of-fit has been tested by applying it to RFX-

mod NVS data, for which b8-15 is about 2÷3 times higher than for VS ones. Figure 2.25 shows that RFX-mod NVS data are also relatively well described. The explicit dependence of τE on b proves the beneficial effect of the boundary control up to the core. The dependence on b is qualitatively in accordance with the Rechester-Rosenbluth (RR) theory of transport in a

stochastic magnetic field, though numerical results [D’Angelo96] based on that theory would

predict a power dependence of -1.5. It has to be noted that the best correlation was obtained

using m=1 modes with n≤-8 while the mode with the highest amplitude is typically n=-7

(usually the central one in RFX-mod). This is in agreement with previous observations that

showed a low effect on stochasticity of the innermost resonant mode.

0

0.5

1

1.5

0 0.5 1 1.5

RFX-mod VSRFX-mod NVS

τ E (m

s)

1.1 10-13 I 1.17 (I/N)-0.35 b8-15

-0.61 (A*Am*T)

Fig. 2.25: Three parameters fit of τE of VS discharges applied to both VS and NVS RFX-mod discharges.


- 23 -

2c.3 Particle transport Interaction between the dynamo modes locks them in phase. The locked mode (LM) produces a

non axial-symmetric deformation of the last closed magnetic surface (LCMS) [Martini06]. The

deformation affects transport introducing non axial-symmetric effects locally modifying both

the density profile and the influx from the wall. Due to the plasma-wall interaction, density

profiles close to the locking position have a steeper edge gradient than at other toroidal

positions [Lorenzini06] and particle influx is

higher [Valisa01]. Controlling the edge radial

magnetic field by VS greatly reduces the

deformation amplitude, but the effect is still

present.

Figure 2.26 shows, as a function of the Ip/N

parameter, the peaking factor (P) defined as the

ratio of the central density to the average

density. In figure 2.26, to avoid LM effect, only

density profile measurements far from locking

position are considered. The data show that

there is no difference on density profiles

between RFX and RFX-mod. This is confirmed by

performing a multivariable regression of the

peaking factor, which gives the scaling

P∝Ip0.14N-0.27 (multiple R=0.7) for RFX-mod data

and a similar one (with a lower correlation) for

RFX.

The negative power dependence on density can be

explained in terms of neutral particle source that

becomes closer to the wall when density

increases. The small positive dependence on

plasma current is less obvious. It could result

from a lower plasma core transport due to a

reduced magnetic stochasticity at higher plasma

currents.

Although density profiles in RFX-mod VS and in

RFX are similar, particle transport is globally

reduced in RFX-mod, particularly at the highest

plasma currents where RFX was strongly affected

by LM. This results from the lower particle influx

of RFX-mod discharges. In RFX-mod particle influx measured at the Hα diagnostic section

shows no correlation with the toroidal position of the m=1 helical component of the LM

0

2

4

6

8

10

12

14

-150 -100 -50 0 50 100 150

Γ H (*

1021

m-2

s-1

)

φo-φHα (°)

(a)

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6

Γ H (*

1021

m-2

s-1 )

ne (*1019 m-3)

(b)

Fig. 2.27: Particle influx for RFX-mod (VS) discharges with plasma current >800 kA. a) Particle influx versus toroidal distance of the m=0 LCMS shrinking from Hα measurement; b) Particle influx versus average plasma density.

0

0,4

0,8

1,2

1,6

0 2 4 6 8 10 12

RFX-mod VSRFX

P=n e

(0)/<

n e>

Ip/N (Am)

Fig. 2.26: Density profile peaking for RFX and RFX-mod VS discharges.


- 24 -

deformation. In discharges with plasma current higher than 800 kA a small increase of particle

influx is present when the toroidal position of the m=0 shrink component of LM deformation is

very close to the Hα measurement section (Fig. 2.27a). On average the influx linearly depends

on the density (Fig. 2.27b) with a value of 3⋅1021 m-2s-1 for a density of 2.5⋅1019 m-3, which

corresponds to a global particle confinement time of about 2 ms. In the same plasma current

range (>800 kA) on RFX about 40% of particle influx came from a region close to the m=1 LM.

Due to the strong wall interaction and the poor particle confinement, in RFX the global influx

was independent of density, with a value ≥6⋅1021 m-2s-1 more than twice than in RFX-mod VS.

Particle transport is simulated using a 1-D transport code that solves the transport equation.

Following the RR theory of diffusion in a stochastic magnetic field, we include in the convective

velocity component of particle flux a velocity proportional to the stochastic coefficient (Dst) and

the normalised temperature gradient:

Vst = -Dst(r)2T(r,t)

∂T(r,t)∂r

To find Dst we parameterise it with five free parameters in the following way:

Dst(r) =(D0- De1)(1-rα)β + De2r30+ De1

The profile of atoms coming from the wall is computed with the Monte Carlo code NENE

(NEutrals and NEutrals). The interaction of the particles with the wall is modelled using the

results of the TRIM code (TRansport of Ion in the Mass), a Monte Carlo code for simulation of

sputtering, ion reflection and ion implantation in structure-less solids.

We evaluate the Dst on RFX and RFX-mod by

simulating the same typical density profile at

=3⋅1019 m-3. For RFX-mod the influx is

ΓH=3⋅1021 m-2s-1 and the exponent of

temperature profile is αT=3; for RFX we use

ΓH=6⋅1021 m-2s-1 and αT=4 because flatter

temperature profiles were found in RFX.

Figure 2.28 shows the diffusion coefficient

and the consequent outward velocity in the

two cases. As it can be expected from halving

the particle influx, the diffusion coefficient of

RFX-mod is approximately halved on the

whole plasma cross-section. Although the

errors in Dst are large, the result seems to

indicate that in RFX-mod the particle

confinement improves on the whole cross-

section as an effect of a simultaneous

reduction of the plasma-wall interaction and

of the core magnetic stochasticity.

0

10

20

30

40

50

60

RFXRFX-mod VS

Dst

(m2 s

-1)

(a)

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

v st (

ms-

1 )

r/a

(b)

Fig. 2.28: Diffusion coefficient and stochastic velocity obtained for RFX (red solid curves) and RFX-mod VS (black dashed curves).


- 25 -

2c.4 Energy transport The introduction of the active control system in

RFX-mod strongly influences plasma thermal

properties. They have been investigated

through the measurements provided by the

main Thomson scattering (TS) diagnostic that

has routinely operated since the beginning of

RFX-mod experimental campaigns [Alfier06a,

Paccagnella06]. In particular, the longer

discharges obtained with the VS, (from ~100ms

to ~300ms), allow to fully exploit the burst of

10 laser pulses of the TS diagnostic, so

increasing the available statistics.

Energy transport is greatly improved in RFX-

mod VS operations. The maximum of the central

electron temperature, Teo, increases nearly

linearly with plasma current up to 1 MA while

RFX showed electron temperature saturation

over 800 kA (see Fig. 2.29), giving a Teo in RFX-

mod VS about 30% higher than in RFX

discharges.

Another consequence of the active control is the

change in the temperature gradients: edge and

core local gradients, ∇Tedge and ∇Tcore, are

obtained by a linear fit of measured points in |r/a|>0.7 and |r/a|~0.5 respectively. ∇Tedge gets

steeper with active control (see fig.2.30). As far as ∇Tcore is concerned, the high spatial

resolution allows also to appreciate a systematic change, with a slight steepening of the core

gradient with the virtual shell passing from an average value of ~0.4 eV/mm in NVS to 0.6

eV/mm in VS.

Higher core electron temperature and steeper edge gradients indicate a decrease of electron

heat transport in RFX-mod VS. An estimate of such a reduction is obtained by applying the 1D

steady state power balance equation [Pasqualotto99]. The effective thermal conductivity, χeff

(Fig. 2.31), is deduced by using the single fluid equation:

χeff = -q⊥(r)/[ne(r)·∇Te(r)]

in which the energy flux, q⊥(r), is evaluated by integrating the expression

∇q⊥(r) = Ω(r) - ε(r)

where Ω(r) = E(r)·j(r) is the ohmic power deposition profile and ε(r) is the experimental total radiation emissivity, mostly localized in the plasma edge and typically ranging from 5% to 20%

Fig. 2.30: ∇Te,ext vs Te(0), at I/N~[3e-14 – 5e-14 ] Am for Ip


- 26 -

of the input power. The current density j(r) profile is reconstructed from external magnetic measurements with the µ&p-model. E(r) is calculated through a local Ohm’s law with Spitzer resistivity, with an effective charge assumed uniform over the line integral of a line-free visible

continuous emission.

Edge radial field control during VS operation (blue profiles in Fig. 2.31) decreases the field

stochasticity in the core, with the effect of slightly reducing the minimum value of χeff by about

20%. Interestingly, the main effect is in the inner region, r/a~[0.5-0.7], where the temperature

gradient is still appreciably non-zero, and the average χeff is about 5 times lower than in the

NVS operation. Even better performances are obtained in the third case (green profiles in Fig.

2.31): it is characterised by low amplitude of all modes at the edge and relatively large

amplitude of the internal n=-7 mode thus realising a QSH state. This causes an increased

electron temperature and the formation of a significant temperature gradient in the core

region, shown in Fig. 2.31. The presence of the helical structure is confirmed by SXR

tomography.

2c.5 High density limit Among the operational limits of magnetically confined fusion plasmas the upper density limit,

peculiar to all major magnetic configurations (Tokamaks, Stellarators, Reversed Field Pinches)

[Greenwald02], is of great importance for its direct impact on fusion performance, which

depends on ne2 f(T), with f(T) a function of the plasma temperature. It has been previously

demonstrated that RFX-mod features an upper density limit remarkably well defined by the

Greenwald’s law found in Tokamaks despite the many differences between the two magnetic

configurations [Valisa04].

The density limit in RFX-mod has been analysed both in its experimental evidences and in

terms of the related edge transport properties in the spirit of a continuous comparison with the

findings in the other magnetic configurations [Valisa06]. In particular, discharges have been

Fig. 2.31: χeff and corresponding Te profiles in three representative profiles, in NVS (brown), VS (blue) and an optimum case (green).


- 27 -

produced near the limit with the aim of analyzing the behaviour of the radiated power, of the

edge plasma parameters and of the edge turbulence, while the trajectory of the plasma

discharge in the high density region has been modeled by means of the 1-D transport code

RITM [Telesca04].

We have found that for RFX-mod the database does not contain discharges with densities close

to the limit and, at the same time, with sustained plasma current, which instead is always

decaying at very high density. According to edge measurements, particle diffusion in the last

few cm of the plasma does not increase in conditions close to the density limit, while the edge

electron temperature does not decrease below 10 eV. The simulations made by RITM show

instead that the mechanism producing the density pump out observed in the experiment is

compatible with a generalized increase of the transport parameters that change mainly in the

core and in the periphery region but not significantly at the very edge. On the other hand, in

RFX-mod the density limit is not a truly

radiation limit in the sense that 100% of the

power input is never radiated: the radiated

power fraction, including the contribution of

the region of the locked modes, reaches

relatively low values, around 30-40 %, at the

highest densities. The origin of the current

decay at values of the density well below the

limit remains to be clarified, but the radiation

pattern in the region of the locked modes seems

a good candidate.

Indeed the width of the radiating layer shown

in Fig. 2.32, poloidally symmetric and

toroidally asymmetric where the plasma

interacts with the wall, appears to erode energy

from the plasma core well inside the reversal

surface and could well be the reason for plasma

cooling, increased resistivity and subsequent current decay, which in the RFP is guaranteed to

be soft by the intimate link between current and toroidal flux. This picture resembles the

MARFE of a Tokamak , with opposite geometry because of the opposite weight of toroidal and

poloidal fields at the edge.

2c.6 Plasma Flow in RFX-mod In RFX-mod, 4 arrays of 10 lines of sight have been recently intalled for performing

spectroscopic measurements of the plasma impurity rotation. During 2006 campaigns the new

systems have been extensively used for collecting data. We focussed particularly on the

Fig. 2.32: (a) reconstruction of the radiated power per unit of toroidal length vs the toroidal angle. The bolometer section is at 00. (b) Tomography of the radiation pattern when, during its toroidal motion, the maximum of the emission crosses the bolometer position at 00. (c) Tomography of the radiated power outside the strong emission peak.


- 28 -

comparison between operations

with and without Virtual Shell

(VS), and on the separate role of

m=0 and m=1 magnetic

perturbations on carbon flow

pattern.

Regarding the first topic, we

observed that while the scaling of

the C V toroidal flow maintains in

both cases the decreasing

dependence on the electron density,

in operations with VS we registered

a clear reduction of the toroidal

rotation velocities (see Fig. 2.33).

C II flow is better suited for

following the behavior of edge flow

pattern in the presence of an external magnetic perturbation. In 2006 we singled out that the

change in the C II toroidal flow direction is related to the presence of the m=0 magnetic

perturbation and its typical deformation of the plasma shape.

2d Edge phenomena

2d.1 Edge turbulence analysis with the Gas Puff Imaging diagnostic. The Gas Puff Imaging diagnostic [Agostini06,

Cavazzana04] is widely used in the RFX-mod

experiment to study the edge turbulence,

measuring the propagation velocity of the edge

fluctuations and characterizing the coherent

structures that are considered the main cause of

anomalous particle transport in the fusion

plasmas. The characterization of the turbulence

was carried out for different plasma conditions,

studying the link between edge fluctuations and

the main plasma density. In Fig. 2.34 the scaling

of the toroidal velocity of the fluctuations as a

function of the plasma density normalized to the Greenwald one is shown. Each black point is

an average over 10 ms during the flat top phase of the discharges; the clear dependence of the

toroidal velocity on the density displays a saturation at about –20 km/s at n/nG >0.35

[Scarin06].

n/nG

vΦ (km/s)

Fig. 2.34: Scaling of the toroidal velocity of the edge fluctuations as function of the density normalized to the Greenwald one. The black dots are the experimental points, the red ones show the average trend.

with VS

w/o VS

Fig. 2.33: C V toroidal flow velocity with and without Virtual Shell operations along line of sights with different impact parameter (colored lines). The figure shows a reduction up to 5 km/s in the inner chords when VS has been operated.


- 29 -

As particle transport at the edge depends on the presence of the coherent structures, the same

scaling with the n/nG parameter was studied for the density of these coherent vortices. Two

methods are applied for counting them. One is based on the continuous wavelet transform and

the Local Intermittency Measurement (LIM)

[Antoni01]; the second method [Sattin06]

assumes that the PDF of the GPI signals can be

fitted by two Gamma functions, one is due to the

uncorrelated fluctuations and the other to the

coherent part. In Fig.2.35 the scaling of the

linear density of bursts measured with the LIM

method, and the coherent fraction of the signal

extracted with the two Gamma functions fit of

the PDF are shown as a function of plasma

density. The two scalings are in agreement: the

edge vortices increase their contribution to the

signals as the parameter n/nG increases. At high density, the turbulence seems to saturate as

shown for the toroidal velocity of fluctuations.

The GPI diagnostic can also provide a 2D imaging of the edge structures with high time

(100 ns) and spatial (5 mm) resolution for the whole discharge duration; as the diagnostic

measures the line integrated emission, a tomographic algorithm is developed. Actually with the

GPI the 2 dimensional evolution

and motion of the edge structures

can be studied. An example of an

inverted pattern is shown in

Fig.2.36.

Due to the unfavorable curvature

of the magnetic lines, fast CCD

cameras (widely used in

tokamaks) cannot be used in the

RFP devices, and the GPI is a

good alternative to them for the

studies of the edge blob.

2d.2 Edge magnetic fluctuation analysis The full set of Integrated System of Internal Sensors (ISIS, [Serianni04]) of magnetic probes

has been put into operation during 2006 and used to obtain a characterization of the high

frequency fluctuations of the three components of the magnetic field (Br, BP, BT). The probes

are located behind the graphite tiles, which form the first wall of the machine, and consist of

pick-up coils measuring the time derivative of the magnetic field. The BT probes are placed in

Fig. 2.35: Scaling of the coherent vortices number as function of plasma density. Red circles: linear density of burst counted with the LIM method; blue squares: fraction of coherent part of the fluctuation measured with the 2 Gamma function

Fig. 2.36: Reconstructed emission profile for one RFX-mod shot. Left: reconstruction with back-projection algorithm; right: inversion with the tomographic algorithm. The vertical black line is the radial position of the vacuum vessel.


- 30 -

one poloidal array in 8 equally spaced positions and in two toroidal arrays, each consisting of

48 equally spaced coils and covering the full toroidal circumference, in two opposite poloidal

positions (top-bottom). The sampling frequency for the BT probes is up to 2 MHz, while the

estimated bandwidth of the measurement is up to 300-400 kHz. An experimental analysis of

the magnetic BT fluctuation levels in different frequency ranges has been performed in a wide

range of experimental conditions.

Various regimes of plasma current density IΦ, I/N

parameter and reversal parameter F have been

explored, along with the dependence of the

fluctuation levels on the Lundquist number S,

which is the ratio of the resistive diffusion time to

the Alfvén time [Zuin06]. Particular attention has

been dedicated to the dynamic behavior of F, as this

is observed in RFX-mod to exhibit large

fluctuations, related to relaxations of the magnetic

field profile during the discrete Dynamo Relaxation

Events (DRE). Moreover, an investigation of the

effect of the Virtual Shell has been performed.

An increase of the magnetic activity related to even

m modes is observed for the low frequency part of

the spectrum when moving from shallow towards

deeper reversal, when the continuous dynamo

action is taken into account. During the discrete

relaxation events, when deeper F values are

dynamically reached, a strong activity with odd m

at high frequency is observed (Fig. 2.37). A

reduction of fluctuation level has been observed to

be induced by the Virtual Shell, with a strong

asymmetrical behavior in the toroidal direction. In particular, the most significant reduction

was observed on the signals taken at the position of the locked mode (Φlock), while the weakest

reduction was measured at Φ>Φlock. It is important to say that the effect is mostly visible in the

low frequency component of the fluctuation, while at frequency above 60 kHz the magnetic

signals seem almost unaffected.

In Fig. 2.38 the power spectra of BT signals obtained in all the toroidal positions are shown in a

color-scale plot. A non axi-symmetric behavior around the locked mode position is observed to

persist despite the action of the VS.

Fig. 2.37: RMS of BT signals from the ISIS system vs F: a) f


- 31 -

In a large set of discharges with active Virtual Shell, an increase of the magnetic fluctuation

with I/N at all the explored time scales has been observed. A robust high frequency activity

with odd m number develops during the discrete magnetic relaxation events. It is found a

scaling of the fluctuation levels with S, comparable with the theoretical numerical prediction

[Cappello96], when the low frequency part of the

spectrum is analyzed, while the magnetic

fluctuations at higher frequency do not show any

clear dependence on S.

By applying the Fourier transform to the signals

from the toroidal arrays, the fast dynamics of the

MHD (tearing) modes can be determined. In

particular, it has been observed that the

development of DREs corresponds to the rapid

formation of a strongly localized magnetic

perturbation at the position of the locked mode.

This perturbation, characterized by a main m=0

periodicity, is then observed to move toroidally,

both clockwise and counter-clockwise, with two

different velocities, as can be seen in Fig. 2.39.

2d.3 Edge Turbulence measurements by probes Similar features have been observed in the edge turbulence of different devices and in

particular bursts on electrostatic fluctuations have been observed in the edge region of several

fusion experiments including tokamaks stellarators and reversed field pinches (RFP). In

different experiment a coherent part has been detected in the edge fluctuations and has been

associated to the presence in the edge region of coherent structures with eddy features or blobs

of density. It is believed that these structures play a major role in driving the transport in the

edge region. In particular in the RFP configuration it has been found that strong bursts,

although representing a small fraction of the signal, carry up to 50% of the particle flux losses.

Turbulence features in the edge region have been investigated by using the new and original

probe system, dubbed “U-probe”. The system is constituted by two blocks toroidally spaced by

about 90 mm, each of them equipped with a matrix 5 (toroidally) times 8 (radially) of Langmuir

pins and a radial array of seven 3-axial magnetic probes. The diagnostics peculiarity allowed a

detailed analysis of the fluctuations both on electrostatic and magnetic quantities with a radial

resolution of 6 mm, the high sampling rate (5 MHz) and the relative bandwidth allowed a high

time resolution as well. Concerning electrostatic parameters the probe provided simultaneously

local measurements of radial profiles of floating potential Vf, ion saturation current, Is, and

electron temperature Te. Furthermore in the same location the three components of magnetic

field fluctuations, Br, Bθ and Bt, have been measured. The probe has been inserted in different

Fig. 2.39: a) Toroidal contour plot of Bt signals from the ISIS system during a DRE (color scale is in Tesla units) b) time behavior of the reversal parameter F.


- 32 -

radial position in order to investigate the edge region up to r/a~0.9, spanning a radial region of

36 mm at each shot. Due to probe insertion the plasma current has been limited to 300-350 kA

with an average plasma density of about 2 1019m-3.

By using the statistical techniques described in [Antoni01] the occurrence of intermittent burst

have been identified in the fluctuation time series. The spatial shape of electrostatic and

magnetic structures have been investigated in the cross field plane (r, phi) by applying a

conditional average technique on a time window including the intermittent events.

An example of this kind

of analysis is shown in

Fig 2.40 where the

positive burst on ion

saturation current, Is,

have been used as

trigger events. It can be

observed that also

radially extended

structures on toroidal

and radial magnetic

field fluctuations are

associated to the

electrostatic ones, with

comparable or larger

size [Spolaore06].

It has been found that a

comparable size

characterizes HeI

emission structures observed by a Gas Puff Imaging diagnostics resolved at 10 MHz

[Cavazzana04, Agostini06] and Is fluctuations structures measured by Langmuir probes. It is

worth noting that the velocity of the structure measured by the GPI system is consistent with

the average E×B velocity measured by the probes, and in particular the time lag between the

structures observed by the two diagnostics is consistent with the hypothesis of a density

structure traveling at the average E×B velocity between their two toroidal locations

[Spolaore06].

The U-Probe system has also been extensively used to investigate the shear flow generation

mechanism, and particularly the turbulence-induced plasma flows via Reynolds Stress

[Vianello05]. The simplest model implying this mechanism may be inferred from an ensemble

average of the momentum balance equation:

Fig.2.40: Conditional average with trigger on positive events detected on Is fluctuations at r=446.5 mm. From top to bottom panels: (Br(r,t)-< Br (r,t)>)/σ (left); (Br (t)-< Br (t)>)/σ at r=446.5 mm (right); analogous quantities for Bt and Is.


- 33 -

φφφφ

φφ νµρµρVVV

BBbbvvV r

rr

rrrt

2

00

~~~~ ∇+⎟⎟

⎠

⎞⎜⎜⎝

⎛−∂=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−∂+∂

where each field has been divided into its average and fluctuating part, and ν is the kinematic

viscosity. The term ⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−=

0

~~~~

µρφ

φφ

bbvvR

rrr is the generalized Reynolds stress,

whereas its velocity and magnetic components are

referred also as Electrostatic Reynolds Stress (ERS) and Maxwell Stress (MS) respectively. Moving the probe on a shot to shot basis, the profiles

of the Reynolds and Maxwell stresses have been

measured for the first time in RFX-mod. In figure

2.41 these profiles are shown together with the E×B velocity profile obtained from floating potential and

temperature measurements. The velocity profile

exhibits a double shear layer. As already observed in

Extrap-T2R [Vianello05] also in RFX-mod it is fairly

evident that the coupling between perpendicular

velocities becomes important inside the plasma,

beyond the nominal positions of the graphite tiles,

where also a strong gradient occurs. Specifically we

are interested in the innermost shear region (r≤ 440

mm) where ERS exhibits a strong gradient whereas

MS is lower with an almost flat profile. The high

spatial and temporal resolution of the

experimental equipment allows also the estimate

of the temporal evolution of the various terms

entering the momentum balance equation. In

particular the temporal evolution of ERS and of

MS has been estimated through the Continuous

Wavelet Transform (CWT) technique [Vianello06].

In Fig. 2.42 a sample from a single shot of the time

traces of φV and of the radial derivates of ERS and

MS are shown. In particular in panel (b) the

comparison between φVt∂ and φvvrr ~~∂ shows the

clear correlation between plasma acceleration and

Fig. 2.41: (a) Drift velocity profiles (b) Total Reynolds stress (c) Reynolds and Maxwell stress profiles. The vertical

2006 activity report - consorzio rfx 2006 activity report technical scientific committee 18 january...

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