Radial Electric Field Formation by Charge Exchange Reaction at Boundary of Fusion Device*

K.C. Lee

U.C. Davis

*submitted to Physics of Plasmas

Contents

1. Introduction2. Assumptions3. Gyro-center shift - Charge Exchange Reactions - Elastic Scatterings4. Comparison with Experiments5. Validity over Quasi-neutrality6. Conclusion

Introduction Motive : H-mode transition analysis developed turbulence suppression by ExB flow Requires the origin of radial electric field : Er

Candidates : Non-ambipolar ion losses [Itoh-Itoh 88’]

- Different from experiment [Burrell 89’]Ion orbit loss [Shaing 92’]

There is no commonly agreed theory for Er formation

Experimental research results :

● Er has peak of -30~ -50 kV/m at core periphery near from separatrix within 100 μsec transition time [Burrell 94’ in DIII-D]● Significant (unknown) correlation between neutrals at edge and H-transition threshold [Carreras 98’ for neutral calculation in DIII-D] • Charge exchange with Neutrals => regarded as ‘friction’ in previous works

Assumptions in Theory of Gyro-Center Shift (1) Toroidal and poloidal symmetry except circular gyro motion of

ions (1-dimensional approach in radial direction)

(2) No transport and MHD activities are included

(3) Ionizations, recombinations and electron involved reactions are neglected (electrons are assumed fixed)

(4) Semi-Steady state

(5) Ti=Te=Tn

Principle of simplicityIf we can describe Er by charge exchange and elastic scattering, other

considerations can be less important

Concept of Reaction Rate

reaction rate density[m-3s-1]

R* = σΦnntarget particle density

= neutral density [m-3]

cross-section(charge exchange)

[m2]

Incident particle flux = nivi

(ion density)x(ion velocity)[m-3][ms-1] = [m-2s-1]

Reaction rate per ion

R [s-1] = σvi nn

R [s-1] : How many reactions could happen per unit time1/R [s] : Average time to be taken before reaction

Gyro-Center Shift by Charge Exchange

hot ion

neutral

core

bou

nd

ary

Gyro-Center Shift Calculation average gyro-center

shift over(-rL ≤ r ≤ rL)per reaction

xreaction rate of an ion with rL and gyro-center

at a point

average gyro-center

shift rate

=

σvi ∫rf(r)nn(r)drσvi ∫f(r)nn(r)dr= (½)rL(n+-n-)/(n++n-)

(½)σvi(n++n-)(¼)σvirL(n+-n-)

current density (charge separation) different from friction[D’lppolito’02]

r

nrv nLi

2

2

1

r

nv

Bq

TnmJ n

ii

iiiGCSr

2

Bq

vmr

i

iL

i

i

m

Tv

2by and

r

nrvenJ nLii

GCSr

2

2

1

Gyro Center Shift by Elastic Scattering

- asymmetry between backward scattering and forward scattering - scattered angle distribution of s-wave scattering from conservation of energy and momentum - 0.53(½)σvirL

2dnn/dr => new coefficient 0.53 is introduced - only less than 15% due to small cross-section at high temperature

Comparison with Experiments

neutral density from Carreras 98’ - emulated data for DIII-D

- profiles were made by cubic polynomials except nn

- nn has exponential decay into core plasma

-separatrix: around R = 2.297m

- calculated for three different temperature profiles; a(500 eV), b(400 eV), c(300 eV)

- cross section data from Thomas & Stacey 97’(±15%)

Result of Calculation

▫ charge build-up rate [Coul/m3sec] showed (-) at core, (+) at SOL

dt

d

r

rJrJ r

r

)(

)(

r

rJ r

)(

• peak dEr/dt value locates around separatrix

• dEr/dt calculated in infinite slab with many ideal assumptions > ~10 times of experimental value (L/H transient time < 100 μsec)

=> Profile shape and absolute value are in agreement with experiments

Discussion on the Calculation Results higher temperature => higher dEr/dt : power threshold of L/H transition

● a scenario of L\H transitionL-mode (high turbulence, low Er)

↓enough heating + proper neutral distribution => dEr/dt ↑

ExB suppress turbulence flow

ne ↑ (pedestal formation)

reduce recycling make stiff nn distribution reduce overall nn

↓dEr/dt ↓( become steady sate with force valence)

↓H-mode (low turbulence, high Er)

Validity over Quasi-neutrality

- electric potential vanishes away out of Debye shielding : screening effect- electric potential is effective inside Debye shielding- when charge build up rate is high enough => all space become field effective- life time of Debye shielding ≡ τD » electron collision time

No. new charges in λD3τD « 1 No. new charges in λD

3τD » 1

Calculated values in the example of experiment are well above the criterion

On the Difference of Charge Exchanges by Gyro-Center Shift and Friction

rni

exinniniinrinr V

meB

vnBVTn

reEJ

2

2

)/(

)(1

r

Tn

nvnmV n

iexinirn

1Where,

r

nTv

Be

menJ n

exii

iGCSr

22 r

nTv

Be

m

n

nJ n

exii

i

nFr

22

Typical value of JrGCS is 300 times larger than Jr

F around separatrix

Gyro-center shift

charge exchange reactions act as cause of the electric field.

Friction

charge exchange reactions act as retardation of charged particle motion driven by existing electric field.

r

nrvenJ nLexii

GCSr

2

2

1

• Miura’92 : neutral energy increase before Hα reduction (200~400 μsec), Toda’97 : neutral injection near x-point triggered H-mode(JFT-2M )

• Burrell’89 : direction of Er is always inward independent of directions of BT, IP and location of x-point (USN/LSN)

• Hazeltine’93 : deuteron plasma is easier in H-mode access than hydrogen plasma, Carreras 98’ etc.

Supporting Experimental Evidences

Conclusion

Gyro-center shift by charge exchange reaction => major source of Er formation

Future work (1) Simulation : combine ‘gyro-center shift’ with existing edge code (UEDGE,

BOUT, etc.) for time transient behavior, poloidal and toroidal aymetryies etc.

(2) Experiment : measure/calculate neutral distribution at edge during the L/H-transition → developing a way to control neutral distribution (and H-mode)

r

nv

Bq

TnmJ n

ii

iiiGCSr

2