Two-Fluid Equilibrium Considerations of T e /T i >> 1, Collisionless ST Plasmas Sustained by RF...

Two-Fluid Equilibrium Considerations of Te/Ti >> 1, Collisionless ST Plasmas Sustained by RF Electron Heating

Y.K.M. Peng1,2, A. Ishida3, Y. Takase2, A. Ejiri2, N. Tsujii2, T. Maekawa4, M. Uchida4, H. Zushi5, K. Hanada5, M. Hasegawa5

1Oak Ridge National Laboratory, UT-Battelle, USA2The University of Tokyo, Japan

3Nishi-Ku, Niigata City, Japan4Kyoto University, Japan

5Kyushu University, Japan

The Second A3 Foresight Workshop on Spherical TorusJanuary 6 - 8, 2014

Tsinghua University, Beijing, PRC

12nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

Two-fluid equilibria approximating RF-driven ST plasmas in TST-2 are calculated for the first time

Motivation: to calculate equilibrium for an apparently new ST plasma regime (TST-2, LATE, QUEST, MAST)– Understand the electron and ion fluid force balance properties

– Provide a basis for orbit, stability, transport, current drive, and boundary studies

Topics:

• Experimental indications of interest

• 2-fluid equilibrium model reduced from first principles

• TST-2 experimental conditions to constrain choices

• Initial results for TST-2 like plasmas

• Improvements in calculations & suggested measurements

• Equilibrium calculations for other ST’s and RF’s


RF-only-driven, inboard-limited ST plasmas in TST-2, LATE, and QUEST share many special features

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• LCFS (----) far within J boundary

• Region of low density (1016-17 m-3) orbit-confined energetic electrons (100 – 500 keV)

• Within LCFS: lower Ti (10 – 50 eV) and Te (50 – 300 eV), collisionless plasmas of modest densities (up to several 1018 m-3)

• Copious keV-level ion or neutral impact sites on tungsten coupons on wall (QUEST)

• High current drive efficiency (0.1 – 0.4 A/W); ~1 A/W on MAST

LATE example2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

Faster loss of energetic electrons than ions would lead to positive plasma potential and substantial ion flow

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• Faster loss of electrons than ions

• Positive “ambipolar” plasma potential

• Sufficiently large radial electric field ion toroidal flow (Er x Bp)

• Substantial centrifugal and electrostatic forces on ions

• For massless electrons of higher Te, -pe = JxB force balance largely retained

Different electron and ion fluid force balance conditions, i.e., two-fluid equilibrium

LATE example2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

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These conditions cause Hall-MHD and one-fluid MHD approximations to lose accuracy


Second order partial differential and algebraic equations of six functionals of poloidal flux are solved

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• Start with continuity, force balance, and Ampere’s law

• Transform in axisymmetric configuration to two 2nd order partial differential equations and six algebraic equations

• Six functionals: Te, Ti, Fi (ion energy), Fe2 (electron energy), K (toroidal magnetic flux), and i (ion poloidal momentum) as functions of and canonical angular momentum Yi()

[Phys. Plasmas 17 (2010) 122507; Phys. Plasmas 19 (2012) 102512]

• Finite-differencing method combined with successive over relaxation (SOR) in progressive multi-grid convergence

• In this work, free-boundary solutions are calculated within a numerical boundary that encloses no coil currents


TST-2 Experiment plasma conditions (shot #75467 @ 60ms) and device constraints

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Data:

• Bt = 1.26 kG, Ip = 10 kA

• Te ~ 300 eV, Ti ~ 10’s eV

• ne ~ 8 x 1017/m3

• Inboard and outboard limiters

• values on numerical boundary interpolated from EFIT that uses flux loop data and modeled vessel eddy current

Assumptions

• Ilcfs ~ 0.6 Ip

• Centrally peaked plasma profiles

Obtain:

• LCFS with elongation = 1.232nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

Relatively simple profile functions are chosen through trial and error - expressions

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(ion poloidal momentum)

),,,;()( 543210 eeeeee TTTTTTe CCCCfCCT

),,,;()( 543210 iiiiii TTTTiTTii CCCCYfCCYT

),,,;()( 543210 iiiiii FFFFiFFii CCCCYfCCYF

)(),,,;()( 2543210 eFFFFFFe FCCCCfCCFiiiiie

),,,;()( 1098762 eeeee FFFFFe CCCCfCF

0)( ii Y

),,,;()( 543210 KKKKKK CCCCfCCK

52

43

45432 1),,,;(

CC

C

xC

C

XCCCCXf

where

CTe0 CTe1 CTe2 CTe3 CTe4 CTe5

0.05 0.50 2.2 0.23 0.05 1

CTi0 CTi1 CTi2 CTi3 CTi4 CTi5

0.005 0.005 2.1 0.23 0.05 1

CFi0 CFi1 CFi2 CFi3 CFi4 CFi5

-0.01 0.12 2.2 0.23 0.1 1

CFe0 CFe1 CFe2 CFe3 CFe4 CFe5

-0.01 -0.12 2.2 0.23 0.1 1

CFe6 CFe7 CFe8 CFe9 CFe10

0.51852 2.2 0.23 0.05 1

CK0 CK1 CK2 CK3 CK4 CK5

2.756 0.0003 5.00 0.23 0.05 1


Relatively simple profile functions are chosen through trial and error – plots & toroidal current density

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-0.06 -0.04 -0.02 0.00 0.02 0.04

-20.0 -18.0 -16.0 -14.0 -12.0 -10.0

-8.0 -6.0 -4.0 -2.0 0.0

X

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Te(X)

-0.06 -0.04 -0.02 0.00 0.02 0.04

-20.0 -18.0 -16.0 -14.0 -12.0 -10.0

-8.0 -6.0 -4.0 -2.0 0.0

X

-0.06 -0.04 -0.02 0.00 0.02 0.04

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-0.06 -0.04 -0.02 0.00 0.02 0.04

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

X

-0.06 -0.04 -0.02 0.00 0.02 0.04 2.754

2.756

2.758

2.760

10*Ti(X)

Fe(X)

10*Ti(X)

K(X)

Te(X) Fe(X)K(X)

10*Fi(X)

10*Fi(X)

)()(1

ln)()Y(

)()Y(

KKRnTT

FFnRj

eii

eii

)()()( 2 eie FFF

• Toroidal current density is set to zero at and beyond the outboard limiter


Initial result: poloidal magnetic flux and toroidal plasma current density

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• LCFS occupies a small area in the vessel cross section (?)

• Jt distributed to the last flux surface defined by outer limiter (?)

• Jt peak located within LCFS and outboard of magnetic axis (?)

• Ilcfs = 0.59 Ip (?)

• Iz ~ 0.05 Ip on midplane (?)

(?) indicates largely arbitrary assumptions

R

Z

RZ


Initial result: electron density and temperature

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• Electron density and temperature peaks located within LCFS and outboard of magnetic axis (?)

• Larger fraction of plasma contained within LCFS

• Finite ne and Te along the inboard numerical boundary (?)

RZ

RZ


Initial result: electrostatic potential, Ti, toroidal electron and ion flow

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• Plasma potential largely confined within LCFS, with peak located outboard of magnetic axis

• Plasma potential drop = 14 V (?)

• Ti max = 10 eV, peak located at outboard edge of LCFS (?)

• Ion flow in co-current direction (?)

R

Z


Initial result: plasma pressure, toroidal current density, Mach numbers, radial electric field, and electron & ion force balance

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• Plasma pressure max ~40 Pa (?)

• Peaked toroidal current distribution (?)

• What is plasma sound speed?

• Large Er shear ion orbit compression

• Electron: largely satisfies pe = -JxB

• Ion (outboard): roughly equal pi, centrifugal, and electrostatic forces balanced by -JxB


Areas of improvement and suggested measurements to further restrain assumed input functions

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Improvements:

• More refined profile function to produce different plasma parameters in and out of the LCFS

• Improve numerical convergence for ion force balance (fig. 6b)

• Longer term: include gyrokinetic effects of energetic electrons

Measurements suggested:

• Shape and location of LCFS

• Currents leaving plasma along open field lines

• Plasma ne, Te, Jt profile information, including along inboard plasma boundary

• Plasma potential, Ti, and ion flow velocity

• Ion Mach number in two-Te plasma [Jones, PRL 35 (1975) 1349]


Next work: comparison between different waves, ECW harmonics, and ST devices

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Different waves and harmonics:

• Plasmas driven by EBW, ECW, LHW, and ICFW (on TST-2)

• Multi-frequency and multi-harmonic heating of electrons (TST-2, LATE, QUEST)

Different ST and vessels:

• LATE: rectangular cross section, metal wall, perpendicular ECW launch with limited polarization control, up to 20 kA driven

• QUEST: limiter and divertor configurations, metal wall, multiple ECW frequencies and harmonics, up to 65 kA driven

• MAST: limiter and divertor configurations, graphite wall, 28 GHz (2nd harmonic), up to 75 kA driven with inboard X-mode launch


Two-Fluid Equilibrium Considerations of T e /T i >> 1, Collisionless ST Plasmas Sustained by RF...

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