PLASMA HEATING AND HOT ION SUSTAINING IN MIRROR

BASED HYBRIDS

V.E.Moiseenko1,2, O.Ågren2,

1 Kharkiv Institute of Physics and Technology, Ukraine2 Uppsala University, Sweden

OUTLINE

• SFLM AND STELLARATOR-MIRROR FDS

• SCENARIOS FOR NEUTRON SOURCE• NUMERICAL MODEL FOR NBI• CALCULATION RESULTS FOR NBI• SCENARIOS FOR ICRH• NUMERICAL MODEL FOT ICRH• CALCULATION RESULTS FOR ICRH• CONCLUSIONS

SFLM AND STELLARATOR-MIRROR FDS

Fusion

Fission reactor

Background plasma

Mirror part

Hot ions

RF antennas

Usage of a open trap for hot ion confinement is beneficial to localize the fusion neutron flux to the SFLM part of the device which is surrounded by a fission mantle. The devices would be capable to operate continuously.It is expected that full control on plasma could be achieved.

Fusion neutron flux

Fission reactor

Background plasma

Mirror part

Stellarator part

NBI

Neutron capturer

Magnetic coils

Stellarator-mirror

SFLM

SCENARIOS FOR NEUTRON SOURCE

•In the first scenario one ion component is hot, and neutrons are produced in collisions with the background plasma ions which are in thermal equilibrium with the electrons. •In this scenario the power balance is determined by the electron drag: The power PTe

-3/2 for the ion heating decreases with an increase of the electron temperature.

•Additional heating of electrons, e.g. with electron cyclotron heating, is less practical because electron heating could be achieved by increasing the hot ion population, which also increases the fusion neutron

output.

Two scenarios of discharge arrangement in mirrors are of interest for the fusion neutron source. Both take advantage of mirror trapping of high energy ions.

In the second scenario, both deuterium and tritium ions are hot.

The background plasma is sustained to stabilize plasma instabilities caused by the non-equilibrium (loss-cone) velocity distributions of the hot ions.

Here, the role of the electrons in power balance is less accentuated, and electron heating would be less

important.

A key problem for the two mentioned scenarios of discharge is hot ion sustaining. This could be made with neutral beam injection (NBI) or radio-frequency (RF) heating in the ion cyclotron range of frequencies.

NUMERICAL MODEL FOR NBI

injcol If

fCl

f

)(v||

1. In the model it is assumed that the hot ions are in minority and collisions of hot ions with themselves are ignored.

2. Another assumption is smallness of the particle drift excursion in perpendicular to the magnetic field direction during collision time.

3. This assumption allows one to consider velocity distributions separately at each magnetic field line and ignore particle perpendicular motion.

The stationary kinetic equation for fast ions reads:

For Maxwellian plasma the collision operator is

ie

col fC,

)(

Fvand

ffffmm

ms

hi

hivvv vvvvvF

2|| v

4

1

2

1

0)/1( mmhis

0)2/(112 x

x/0|| 32

22

0 v

4

hi

hi

m

nee

T

mx

B

2

2k

v

x

dttt0

)exp(2

.

indices hi and =e,i denote hot ions, electrons and

background ions respectively

NUMERICAL MODEL (cont.)If (collision time)/(bounce time)>>1 ),( ff

New variables : himB /2v 00 himB /2v 00||

r

l

r

l

r

l

r

l

l

l

injinjl

l

l

l

colcoll

l

dlIIdl

dlfCfCdl

||

0||0||

1

||

||

0||0||0||0||

1

||

v

)v()v(

v

v

)v(/)v()v(/)v(

v

Bounce averaging

In the code, time is expressed in units of ion-ion collision time for the background ions. The velocity is normalized by the background ion thermal velocity.

CALCULATION RESULTS Regular parameter set: 100)/( TkEE Binjinj

100mir 1stmagnetic field depends parabolically on the longitudinal coordinate

the mirror ratio is chosen as R=1.7, NBI generates ions with perpendicular energy at R=1.3. NBI energy spread is chosen as 1E

For this parameter set the average normalized ion energy is 34hiE

The electron drag takes 62% of the injected power, the ion-ion collisions 19%. The remainder goes to the loss cone and is lost due to finite confinement time at the mirror part of the device.

Contours of distribution function. Dashed line shows boundary between trapped and passing particles.

A change of the mirror ratio from R=1.7 to R=2 increases the hot ion content only by 1%, and the mean ion energy also remains almost unchanged.

1 2 3 4 5 6

N orm alized para lle l ve loc ity

1

2

3

4

5

6

7

8

Nor

mal

ized

per

pend

icul

ar v

eloc

ity

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

CALCULATION RESULTS (cont.)An increase of the ion confinement time at the mirror part from 100mir

1000mir results in a hot ion density increase by 10%, and this valueto

does not change significantly with further increase of this parameter.

Confining properties of the stellarator are also not very sensitive: A decrease of the stellarator confinement time from 1st to 3.0st

results only in a decrease of hot ion population by 4%.

0

0,2

0,4

0,6

0,8

0 2 4 6

Background temperature, keV

Fusi

on Q

Einj=200

Einj=100

Dependence of fusion Q on background plasma temperature for

two normalized injection energies. -1,5 -1 -0,5 0 0,5 1 1,5

Normalized length

Net

ron

flu

x lin

e d

ensi

ty, a

.u.

T=3 keV

T=0,8 keV

Neutron emission line intensity for Einj=300keV and two different background plasma

temperatures.

If the fission mantle is located at |l|<0.5, the relative portion of the neutrons emitted in this zone is 61% for T=3 keV and 57% for T=0.8 keV.If -0.5<l<1 this portion rises to 80%

SCENARIOS FOR ICRH

plasma

FMSW cut-off

Alfven resonance cut-off

Deuterium cyclotron surface

Conversion surface

FMSW FAW FMSW

antenna

Minority heating:

Wave is launched by antenna near cut-off

Wave does not propagates to high field side reflecting from cut-off

FMSW then converts to FAW

Alfven resonances are also excited

FAW is absorbed owing to cyclotron damping

Second harmonic heating:

The same, but no conversion to FAW and no Alfven resonances

Conversion to IBW is possible

RF field forms a standing wave in radial direction and propagates along magnetic field towards midplane

V.E. MOISEENKO, O. AGREN, Phys. Plasmas 12, ID 102504 (2005).V.E. MOISEENKO, O. AGREN, Phys. Plasmas 14, ID 022503 (2007).

Scenarios for ICRH (cont.)

(a)

(b)

(c)

(d)

(e)

-20.00

0.00

20.00

x

-20.00

0.00

20.00

x

-20.00

0.00

20.00

x

4100.00 4150.00 4200.00 4250.00 4300.00 4350.00 4400.00 4450.00 4500.00

z [cm ]

-20.00

0.00

20.00

x

-20.00

0.00

20.00

x

-20.00

0.00

20.00

x

-20.00

0.00

20.00

x

-20.00

0.00

20.00

x

720.00 740.00 760.00 780.00 800.00 820.00 840.00 860.00 880.00 900.00

z

-20.00

0.00

20.00

x

-20.00

0.00

20.00

x

Power

Re Ex

Im Ex

Re Ey

Im Ey

The SFLM neutron source has a substantially smaller size than a fusion reactor machine. In this situation the fast magnetosonic wave which is excited by the antenna makes fewer oscillations across the magnetic field.

The width of the ion cyclotron zone becomes smaller owing to the sharper gradients of the magnetic field magnitude along magnetic field lines.

The last factor is softened by a smaller mirror ratio.

Reactor Neutron sourceSecond harmonic calculation

NUMERICAL MODEL

extik jEεEeeE 020|||| ˆ

Zero electron mass approximation is chosen in which the parallel component of the electric field is neglected in Maxwell’s operator

)exp(

2)(1 2

||||

2i

Fvk T

p

WKB formulas for cyclotron damping: fundamental harmonic

||||/ Tc vk,

Second harmonic

EeEeEeeD ||22||2||||0~

4

1~8

1~8

1/ i

)1/)(/21(1)exp(2

)(4~ 2

||22

222||||

22

2

TTc

cT

Tp vvi

Fvk

v

||||2 /2 Tc vk V.E. MOISEENKO, O. AGREN, Phys. Plasmas 14, ID 022503 (2007).

0nEBoundary conditions

0)()(

zwz ikz

eEeE

PARAMETERS OF CALCULATIONS

In the numerical calculations, the following regular set of parameters is chosen: Plasma density (in its maximum) is

14

0 10en cm-3, heating frequency is 8101.21.1 s-1, deuterium and tritium parallel and perpendicular thermal velocities at the z -axis are 5

|||| 105 TTDT vv m/s and 61035.1 TTDT vv m/s, the deuterium concentration is

4.0DC , 2.0|| k cm-1 and 15.0wk cm-1.

We choose the antenna height as 9xl cm, the antenna width as 10zl cm and the antenna length as 130yl cm. The regular

position of the antenna with respect to the center of the trap is 845az cm.

Plasma radius at the central plane where the magnetic surfaces

have a circular cross-section is a=40 cm, magnetic field value at

the midplane is B0=2 T, the trap length is L=18 m and the mirror

ratio at the trap ends is R=2.3.

CALCULATION RESULTS (MINORITY HEATING)

1E+8 1.2E+8 1.4E+8 1.6E+8

0

4

8

12

16

20

2/2 IPr displ

dVEpPdis

Im2

202 sΠΠ dPfl )( 2

flpltot rrr

Dependence of the absorption (solid line) and shine-through (dashed line) resistances on RF heating frequency.

6E+13 8E+13 1E+14 1.2E+14 1.4E+14

0

4

8

12

16

20

Dependence of the absorption and shine-through resistances on plasma density.

CALCULATION RESULTS (minority heating)

840 860 880 900 920

0

10

20

30

Dependence of the absorption and shine-through resistances on antenna location.

CALCULATION RESULTS (second harmonic heating)

1.4E+8 1.6E+8 1.8E+8 2E+8 2.2E+8

0

4

8

12

16

20

Dependence of the absorption (solid line) and shine-through (dashed line) resistances on RF heating frequency.

6E+13 8E+13 1E+14 1.2E+14 1.4E+14

0

4

8

12

16

20

Dependence of the absorption and shine-through resistances on plasma density.

CALCULATION RESULTS (second harmonic heating)

840 860 880 900 920 940

0

10

20

30

7E+7 8E+7 9E+7 1E+8 1.1E+8

0

4

8

12

16

20

Dependence of the absorption and shine-through resistances on antenna location.

Dependence of the absorption and shine-through resistances on tritium thermal velocity.

CONCLUSIONS• Hot ion sustaining is most important for mirror and stellarator-mirror

fission-fusion hybrid devices. Efficient methods for this are NBI and ion cyclotron resonance heating.

• According to the numerical results for NBI in a stellarator-mirror hybrid, the hot ion population depends only weakly on the confinement of the stellarator part.

• At the mirror part, it is sufficient to confine the hot ions for only a few hot ion-background ion collision times.

• The mirror ratio of the local mirror trap which is sufficient to avoid substantial ion losses is small, a value R=1.7 is adequate, and increasing it does not result in a considerable increase of the hot ion population.

• The calculated axial distribution of the neutron flux peaks at the

injection points and has a noticeable magnitude at locations between the peaks. About 60% of the flux reaches the fission mantle if the NBI is made from both sides of the nuclear core. This amount rises to 80% for single-side NBI. It could be further increased by a steeper magnetic field profile near the injection area and making the field more uniform in the remaining mirror part.

CONCLUSIONS (cont.)• The calculations for the straight field line mirror hybrid show

good performance of deuterium minority heating at the fundamental ion cyclotron frequency. The heating is not strongly dependent on the ion temperature and, therefore, has no start-up problem. The sensitivity to other factors, e.g. plasma density, antenna location etc., is not critical.

• Second harmonic heating of tritium is always accompanied by a

noticeable shine-through beyond the tritium second harmonic resonance zone. However, the wave power would not be wasted, since the shined-through wave encounters deuterium second harmonic cyclotron resonance on its way to the midplane. Most of the remaining small wave energy may also be absorbed at the tritium second harmonic resonance zone near the opposite mirror.

• The second harmonic heating calculations predict relatively sensitive dependence on plasma density, antenna location and tritium temperature. However, if the necessary conditions are provided this heating is satisfactorily efficient.

Thank you!