Hard Xray Diagnostic for Lower Hybrid Current Drive on Alcator C-

Mod

J. Liptac, J. Decker, R. Parker, V. Tang, P. Bonoli MIT PSFC Y. Peysson CEA Cadarache

APS 2003 Albuquerque, NM

Abstract

•A Lower Hybrid Current Drive (LHCD) system is being installed on C-Mod allowing the exploration of advanced tokamak (AT) regimes through current profile control

•The LH current profile may be inferred through non-thermal Bremsstrahlung emission measured by a pinhole camera

•A Fokker-Planck (FP) model coupled to camera data gives information about the LH modified electron distribution function

•Camera design and FP model will be discussed

LH Waves

LHCD works through electron Landau damping around v~3vth

LHCD is calculated based on•Ray tracing•Imaginary part of the hot plasma dispersion relation or an FP solver•k|| =(krBr+m/rBθ+n/RBφ)/|B|

•Creation of non-thermal Bremsstrahlung radiation from high energy tail

Experimental verification of LHCD location is needed

Bonoli ACCOME Simulation

Non-Thermal Bremsstrahlung

Bremsstrahlung radiation is continuous: an electron of energy E can radiate any hν < E

•No direct measure of distribution function, need model•e-i Bremsstrahlung is typically an order of magnitude larger than e-e for E < 500 keV•Radiation is anisotropic, peaked in the forward direction

0 5 10 15 20−8

−6

−4

−2

0

2

4

6

8

Total Bremsstrahlung Cross−section (cm2 x 10−28 )

Parallel Direction

Per

pend

icul

ar D

irect

ion

10keV20keV50keV100keV

Eelectron = 200 keV

A

B

C

D

E

K

J

G

F

H

Experimental Layout

LH AntennaKlystrons

HXRDiagnostic

Wave Guides

C-Mod top view

•Located on mezzanine•12 klystrons at 250kW each → 3MW•f = 4.6GHz

•Located on C-port•Grill composed of 96 waveguides, 4 rows of 24•Dynamic phase change possible, ~ms, allowing for pre-program spectra or feedback control

•Located on B-port•32 channel pinhole camera•20-250keV energy range•~1.5cm spatial resolution•~10ms temporal resolution

HXR Camera Design32 channel pinhole camera1 using CZT detectors and fast digitization techniques2

C-Mod cross section with HXR camera

HXR Camera Design (cont.)CdZnTe detectors:

•Flexibility through software data analysis•Energy resolution limited by detector•Improved noise rejection/pile up detection•Lower system cost•Possibility of real time feedback control of n||

Fast digitization allows:

Data management:

•High Z 49.1, high density 5.8g/cm3 •No cooling or magnetic shielding•Made in the USA- eV Products

•Up to 2GB/shot raw data•~150 shot scratch disk•Local data processing•Processed data archived

HXR Camera Design (cont.)

Aluminum RF shield and inner structural support

Lead plate shielding variable thickness

Square pinhole

Insulated support structure Cable feed through

Aluminum vacuum window

B-port

Pulse Processing

Preamplifier

Photons

Detector Amplifierand

Shaper

FastDigitizer

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

5

10

15

20

25

30

35

40Detector Current vs Time

Time (µs)

Cu

rren

t (n

A)

Ie

Ih

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5Preamp Voltage vs Time

Time (µs)

Vo

ltag

e (m

V)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Gaussian Shaper Output

Time (µs)

Vo

ltag

e (V

)

•Energy resolution better than 10% at 60kev•Charge transport limits count rates to ~1MHz

•High sensitivity ~120mV/MeV•τf =1ms•Small size 2.6×1.5cm

•Developed in house•~1µs pulse width•DC offset•Line driver•Small size 2.5×7.6cm

DTACQ ACQ216

•CPCI form factor•16ch/board at 10MHz•1GB/board memory•14 bit resolution

eV Products 5×5×2mm CZT

eV Products eV-5093 Preamp

Gaussian Shaper

Shaping Electronics

•No undershoot → better energy performance at high count rate•Easy to fit → reduces pile up and improves rejection

Time (us)

0 0.5 1.0 1.5 2.00

100

200

300

400

Volt

age

(mV

)

Vdiff

V1

V2

V3

Gaussian pulse shape3:

Shaper step response from PSPICE model

+5

DC_LD

-5

+5 +5

-5-5 -5

+5

PRE_IN

-5

V_OFF

+5

DC_LD

OUT

C30 0.01uF

C31 6.8uF

C38

0.1uF

U2

LMH6702/SOT23_5

3

4

52

1

+

-

V+

V-

OUT

R15

23.7

U1

LMH6702/SOT23_5

3

4

52

1

+

-

V+

V-

OUT

R22 237

U4

LMH6702/SOT23_5

3

4

52

1

+

-

V+

V-

OUT

R4 10

R23 237

R17

237

C23

270pF

R1 10

C20

3300pF

C7 6.8uF

U5

LMH6702/SOT23_5

3

4

52

1

+

-

V+

V-

OUT

R13 237R11 237

C5 470pF

C13 0.01uF

C4 330pF

C15

0.1uF

C16

0.1uF

C34 6.8uF

C35 6.8uF

C9 6.8uF

C40 6.8uF

C6 6.8uF

R21

1KC39 0.01uF

C32 6.8uF

C2 180pF

C3 330pF

R5 90.9R3 137

U3

LMH6702/SOT23_5

3

4

52

1

+

-

V+

V-

OUTC17

0.1uF

R24

23.7

C29 0.01uFC27 0.01uF

R19 10

R14 237

C26

470pF

R9 365R2 90.9

C25

180pF

R8 90.9

C14

1800pF

C12 0.01uF

C28 0.01uF

C22

330pF

C18

0.1uFC21

3300pF

R7 10

R12 237

Q1MMB3904

C8 6.8uF

C37

3300pF

C11 0.01uF

R18

237

C36 0.01uF

R6 267

C19

3300pF

R10

49.9

C1 270pF

R16

237

C33 6.8uF

R20 49.9

C24

330pF

C10 0.01uF

Vdiff

V1 V2V3

Shaping Electronics (cont.)

Gaussian shaper realized through Sallen-Key filter and surface mount PCB

•Flexible gain and pulse width•DC offset used to adjust signal into digitizer range of ± 2.5V•50Ω line driver

0 0.2 0.4 0.6 0.8 1-2

0

2

4

6

8

10

12

14Current Profiles

Normalized Radius (r/a)

Cur

rent

Den

sity

(M

A/m

2 )

Total 804 kALH 390 kAOH -27.7 kABS 434 kA

0 0.2 0.4 0.6 0.8 10

1

2

3

4Density Profile

Normalized Radius (r/a)

Ele

ctro

n D

ensi

ty (

1020

/m3 )

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10q Profile

Normalized Radius (r/a)

Saf

ety

Fac

tor

0 0.2 0.4 0.6 0.8 10

2

4

6

8Temperature Profiles

Normalized Radius (r/a)

Tem

pera

ture

(ke

V)

Te

Ti

Count RateCount rate estimated through AT target plasma parameters and a crude average over the emissive region

∑∑ ∆∆=k i

ikdc

e lhhrjdaanN νν ),(2

222

.Count Rate:

ac = collimator sizead = detector sized = pinhole to detector spacing

Count Rate (cont.)

0 50 100 150 200 250 30010

0

101

102

103

104

105

106 Count Rate vs Energy

Energy (keV)C

ount

Rat

e (1

/s)

•Spatial resolution linked to count rate through aperture size•∆hν is set by bin size, or detector resolution•Larger energy bins increase the number of counts per channel at the expense ∆hν•Temporal resolution determined by statistical accuracy needed

Spatial, temporal, and energy resolution are interdependent through counting statistics

30 35 40 45 50 55 60 65 70 75 8010

3

104

105

106

Pinhole to Detector Spacing (cm)

Co

un

t R

ate

(1/s

)

Count Rate and Resolution vs Pinhole to Detector Spacing

E=20-250 keV

E=35-250 keV

E=50-250 keV

30 35 40 45 50 55 60 65 70 75 801.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

Res

olu

tio

n (

cm)

ac=0.5cm

Spatial Resolution

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

3

104

105

106

Aperture size (cm)

Count

Rat

e (1

/s)

Count Rate and Resolution vs Aperture Size

E=20-250 keV

E=35-250 keV

E=50-250 keV

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Res

olu

tion (

cm)

Resolution Mapping Resolution Mapping

ac=0.5cm

d=39cm

Spatial resolution:Estimation: ∆r ~ 2a / #chords=1.4cmGeometry: ∆r = (1 + D/d)ac ~ 1.7cm

Plasma

D d

ac

ad

Shielding

Diagnostics on B-port redesigned giving more room for shielding

2 4 6 8 10 12 14 16 18 20 2210

0

101

102

103

104

105

106

Background Count Rate vs Channel

Channel Number

Count

Rat

e (1

/s)

Background measurements indicate gamma shielding is required

•2cm minimum Pb for gammas•Al RF shield

•Neutron shielding may now be considered

Background measurement using pixilated detector and ASIC shot 1030605017 from t = 0.975-0.985

MCNP will be used to investigate tradeoffs in shield design

Neutron Rate 7.5e13 (1/s)

Pulse Height Analysis

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

5 Count Rate vs Channel

Channel Number

Count

Rat

e (1

/s)

No ShieldingNeutron Rate 7.5e13 (1/s)

Software analysis:•Variable time and energy binning → adjust depending on count rate giving more data points for acceptable statistics•Gaussian fitting → double peaks fitted to reduce pile up and increase effective count rate

Background measurement using pixilated detector and ASIC shot 1030605017 from t = 0.975-0.985

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Digitized Signal

Time (us)

Volt

age

(V)

)

Digitization Rate = 6MHz

Reconstruction

•MATLAB GUI developed for Tore Supra HXR analysis is being adapted for C-Mod

HXR measures the line integrated emissivity and a reconstruction4

is needed to recover the radial profile

Reconstruction methods include:•Abel inversion•Minimum Fisher•Maximum entropy•And others

Distribution Function Model

-5 0 5 10 15

-2

0

2

4

6

8

10

12

14

16

ppar/pth-ref

pper

p/pt

h-re

f

2-D steady state electron distribution function

FPCode

Local plasma parametersT, n, Ip, Zeff

LH parametersDql, vmin, vmax

fe(p||,p⊥)

Code written by J. Decker and Y. Peysson

Physical interpretation•Dql → LH power level

•vmax → Wave accessibility

•vmin → Landau damping

LH distribution function model5 coupled with a FP calculation gets at the underlying physics while including collision and the Ohmic field

LH model

0 50 100 150 200 25010

-32

10-31

10-30

10-29

10-28

10-27

10-26

10-25

Local Emissivity

Energy (keV)

Em

issi

vity

(m

3 s-1 s

r-1 keV

-1)

HXR Calculation

Thermal emission

Tphfe(p||,p⊥) HXR

Code

Once the distribution function is known then the local emissivity may be found given the Bremsstrahlung cross sections and the viewingangle

θv

Local j(hν)

)exp(0

phTh

hA

dhdtddn ν

νν−=

Ω

Tph is the characteristic slope of the emission and is related to the count rate by:

Summary

•A 32 channel CZT detector pinhole camera using fast digitization has been developed to measure the 20-250keV electron population resulting from LHCD

•Emissivity profile reconstruction gives the LHCD location

•Measurements coupled to a FP model give information about the electron distribution function and are directly related to wave accessibility and power level

•Camera will be ready for operation when LH is installed

References

1 Y. Peysson and F. Imbeaux Rev. Sci. Instrum. 70(10) 3987 (1999)

2 R. O’Connell et. al. Rev. Sci. Instrum. 74(3) 2001 (2003)

3 Ohkawa et. al. Nuc. Instrum. Meth. 138 85 (1976)

5J. Decker and Y. Peysson 29th EPS Montreax 26B(P-4.052) (2002)

4 Anton et. al. Plasma Phys. Control. Fusion 38 1849 (1976)