D. Tskhakaya, LH SOL Generated Fast Particles Meeting IPP.CR, Prague December 16-17, 2004 Quasi-PIC...

D. Tskhakaya, LH SOL Generated Fast Particles Meeting IPP.CR, Prague December 16-17, 2004

Quasi-PIC modelling of electron acceleration in front of the ITER LH

antenna

D. Tskhakaya

Plasma and Energy Physics Group, Association Euratom – ÖAW, Department

*Permanent address: Institute of Physics, Georgian Academy of Sciences,Tbilisi, Georgia

Outline of the Talk

• Introduction

• “Quasi”-PIC model for electron acceleration

• Results for CASTOR and Tore-Supra

• Preliminary results for ITER

• Conclusions



Introduction

Different models of particle acceleration in front of LH antennas

“Quasi”-PIC simulations Electron motion in the “exact” field [Tskhakaya]

Test particle simulations Electron motion in the “near-field” approximation [Fuchs]

PIC simulations (i) Electron time scales [Rantamäki](ii) Ion time scales [Tskhakaya]

Fluid simulations 3D fluid model [Petržilka]


c

LwgR

4

2

mm

mmmm

ITERR

TSR

CASTORR

7.0

,6.0,5.0

The near-field approximation

only inside the Rayleigh zone

The experimentally observed electron beam width: 2-5 mm.

Introduction


Quasi-PIC model

dkkztikrEtzrE

k

z )exp),(Re),,( wg1

Plasma

z

r

wg2 wg4 wg3

Boundary conditions Simulation area

In the cold plasma approximation, neglecting coupling

between the slow and fast waves we have

Lr

krEckkrEr

pp

p

/1

,0),(1//),(

20

2

222222

2


Quasi-PIC model

Schematic of quasi-PIC simulation of electron acceleration in front of the LH grill.

0kE i) can be obtained from a self-consistent

plasma – slow wave coupling code (e.g., SWAN)

ii) A simple analytic approximation can be used (for example the TEM field)

Code calculating slow wave

Input: n, w, L, E (r=t=0)z

Output: A(r, z), B(r, z)

E (r,z,t)=Acos(wt)+Bsin(wt)z PIC

dkzzzktirK

KE

dkkztirH

HElrtzrE

ck

k

ck

kz

222

222

/

03/1

3/10

/

)2(3/1

)2(3/10

exp0

exp0

/1Re),,(

3222

0 /

3

2

LrL

ckp


Results for CASTOR and TS

CASTOR: Near-field approximation

CASTOR: exact field



The time needed to reach the stationary state after “switching

on” the LH grill is defined by the average electron fly time in

front of the grill, and can be from 60 (CASTOR) to 500 (TS)

0 100 200 300 400 500 600 7000.4

0.5

0.6

0.7

0.8

0.9

1

TLH

N/N0

CASTORTS (E

0=5 kV/cm)

TS (E0=3 kV/cm)

Time evolution of the number of simulation particles [Tskhakaya 2002].



0 1 2 3 4 5 6 735

40

45

50

55

60

65

70

75

r [mm]

E [ev]

near-field modelexact LH fieldwithout LH field

0 2 4 6 850

100

150

200

250

300

350

400

450

500

550

r [mm]

E [ev]

exact LH fieldexact LH field including high n

|| damping

without LH field

Radial profiles of the average energy carried by electrons having been accelerated in front of the grill.

Energy absorbed in the “first peak”:

CASTOR Tore Supra

rpolebfabs LTEEP )4(

TSLH

TSabs PkWP 02.060 CASTOR

LHCASTORabs PkWP 01.06.0


Preliminary results for ITER

PAM support structure

Plasma end

DETAILED DESIGN DESCRIPTION LOWER

HYBRID HEATING AND CURRENT DRIVE SYSTEM

Number of launchers 2

Power per launcher 20 MW

Power density (active wg) 33 MW/m2

Working electric field < 6.2 kV/cm

Number of PAM (per launcher) 4

Number of active/passive wg per PAM 24/25

Width of active/passive wg (mm) 9.25/ 7.25

Type of the modes TE01+TE02+TE03

Frequency 5 GHz

by Ph. BIBET, G. BOSIA (2001)



0 0.5 1 1.50

100

200

300

400

500

600

R [mm]

Em

ax [

eV

]

Maximum final energy vs “rounding” radius, R.Case with E0=4 kV/cm. [Bibet 2001]

3.75Frequency GHz

33Width of septa mm

07.25Width of passive waveguide mm

7.59.25Width of active waveguide mm

3224Number of waveguides

SimulationITER PAM

90°270°Phasing



The “exact” toroidal electric field in front of ITER LH antenna.

n|| < 500. n|| < 40 (corresponds to R=1.5 mm)



0 500 1000 15000

100

200

300

400

t/TLH

eV

<E>LHS

<E>RHS

Average energy of electrons vs timeNumber of simulated electrons vs time

Results for near-field approximation

0 500 1000 15000.2

0.4

0.6

0.8

1

t/TLH

N/N

0



0 500 1000 1500 2000 2500

10-6

10-4

10-2

100

E [eV]

f(E)LHSRHSE

LH=0

Electron distribution function


Conclusions

• The results obtained indicate that the radial width of the high

energy beam observed experimentally (2-5 mm) can be explained

as a combined effect of the radial structure of the ”electric field in

front of the grill and of the damping of high n|| modes by

accelerated electrons

• For studying of electron acceleration time periods of a few

hundreds of LH wave periods are required

• The average energy of electrons accelerated in front of the ITER LH

antenna (with a sharp septa) should not exceed 400 eV.

• Future plan: To complete simulations with the “exact” field and

study effect of rounding of the septa.

D. Tskhakaya, LH SOL Generated Fast Particles Meeting IPP.CR, Prague December 16-17, 2004 Quasi-PIC...

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