Black Aurora, Bohm Diffusions, Quasi-Neutrality Mysteries Explained

Kwan Chul LeeNational Fusion Research Institute (NFRI), Daejeon, Korea

1Feb. 7, 2019, PPPL, Theory Seminar

Introduction to Gyro-Center Shift (GCS) by ion-neutral collisions

2

1. GCS theory explained Er formation at tokamak boundary [K.C. Lee, PoP 2006]

2. Explained reversed motion of cathode spot in arc discharge [K.C. Lee, PRL 2007]

3. Explained L/H transition & turbulence induced diffusion [K.C. Lee, PPCF 2009]

4. Measurement of turbulence induced diffusion on NSTX [K.C. Lee, et al., JKPS* 2013]

5. Analysis of quasi-neutrality violation by ion-neutral collisions [K.C. Lee, JKPS* 2013]

6. Analysis of Bohm diffusions by GCS theory [K.C. Lee, IEEE* 2015]

7. Measurement and analysis of poloidal rotation on KSTAR [ IAEA FEC 2014]

8. .Black aurora and EEJ analysis by GCS theory [Kwan Chul Lee, PoP 2017]

33

There are thousands times more collisions among ions and electrons (such as between passing particles and trapped particles). Why is ion-neutral collision so important?

-Collisions between charged particles cannot change the speed of ExB train. (cannonball in a railway carriage)-Neutrals are not influenced by B-field or E-field,

-ExB train is in perpendicular direction, -Collisions between charged particles can change in parallel direction, ex: bootstrap current

ExB train

ExB of electrons and ionsare same in tokamak

44

Contents

1. Gyro-Center Shift(GCS) current

2. 4 examples of E-field formation

3. Origin of Bohm diffusions

4. Reynolds number of ion-neutral friction

5. Turbulence induced diffusion and L\H transition

6. Criterion of quasi-neutrality by charge exchange

7. Summary and future works

5

* inii mnBJ

nini n *

plasma

B chargeexchange

Radial current by ion-neutral collision

)

6

rn

nr

dn

dnn

niLi

nicx

niicxav

1

21

)(

)()(

ry iii ˆsinˆcos

nini n reaction rate =

n

ni

eBnnkT

v* by neutral density gradient

expectation value

7

(K.C.Lee, PoP 06’)

),1(n

ni

i

i

ni

Lii

GCSr n

neBkT

nP

eBBErenJ

02

E,dtdJ

Example 1: Er well of tokamak

(DIII-D)

8

Er well of NSTX

▶Neutral density profile is analyzed by tangential camera data and DEGAS2 code[D. P. Stotler et al PoP 2015]

▶Er measurement provided by ERD: R. Bell

▶Er calculation by GCS current agreed withmeasurement

NSTX #142214: 0.4 sec

9

general form of for weakly ionized/magnetized plasmas ( )GCSrJ niLir ~

)(/11

22iniLi

D qBnp

BE

r

probability of ions to have longer mean free path than ion gyro-radius

])exp()(11[ 2

n

nin

i

ii

GCSr qBn

nkTqBnP

BEqnJ

nicici

ni

ni

Lir

1

nni n1

for weakly ionized cases GCSrJ

10

(1991)

- first found by Stark 1903- no explanation for both pressure

and B-field dependence until 2007

reversed motion of cathode spots in arc discharges

11

► reversed motion of cathode spots in arc discharges

70’

[K.C. Lee, PRL 2007]

])exp()(11[ 2

n

ni

i

ii

GCSr qBn

nkTqBnP

BEqnJ

ni

Lir

~200m/sec westward (day time) neutral wind measured (Hysell JGR 2002)

► equatorial electrojet (EEJ)- east-west current structure on magnetic dip equator- fluctuations with daily reverse- extensively measured and studied [Forbes, 1981]- difference of ion drift and electron drift of ExB

generates Hall current (missing: origin of Er)

)(1 2 ni

GCSr B

EqnJ

(satellite measurement Kelly 1989)

earth

Dynamo [Rishbeth,1997]

1313

black aurora simply represent the absence of aurora

counterpart of EEJ in polar region: polar electro-jeta.k.a : aurora

14

Swedish satellite Freja observed strong cross E-field on black aurora [Marklund, PPCF 1997]

Strong E-field is found across the black aurora

15

𝑞𝑛𝜔 𝜏

𝐸𝐵

𝛻𝑃𝑞𝐵𝑛

𝑘𝑇𝑞𝐵

𝛻𝑛𝑛 0

𝐸 𝑘𝑇 𝑞𝐿⁄

Agreements: 1. polarity2. magnitude3. inversely proportional to scale length

[Kwan Chul Lee, PoP 2017]

16

short circuit effect

qJ GCS /

nnii nnnn //

Bohm experiment : 401

131

ni

Lir eB

kTD i)

201~

71( eB

kTD eB 16

1

Simon experiment : 131

ni

Lir

measuredD=0.92 m2/s

GCS theoryD=0.74 m2/s

E => 0, short circuit effect :

approximation of

Γ D𝛻𝑛

),1(n

ni

i

i

ni

Lii

GCSr n

neBkT

nP

eBBErenJ

Γ 𝑛𝑟𝜆

𝑘𝑇 𝛻𝑛𝑒𝐵𝑛

𝑘𝑇 𝛻𝑛𝑒𝐵𝑛

𝐷2𝑟𝜆

𝑘𝑇𝑒𝐵

[Goldston, 1995]

origin of Bohm diffusions

[Simon, 1959]

17

GPI fluctuation analysis on NSTX [Diallo et al. NF (2017)]

- poloidal velocities do not change prior to the L-H transition- Reynolds work may not be large enough to explain the L-H

transition on NSTX, contrary to the predator-prey model.

What is the real mechanism for L-H transition?

-learning by analogy

-in neutral fluidsturbulence acts as asource of friction

-at tokamak boundaryEr increases in H-mode

18

iLi

nini

iniii

Liii

rkTeB

mnrmn

**

**Re2

Inertial force

viscous force

Re > Re* : turbulent flow Re < Re* : laminar flow

Re*: critical Reynolds number

Re* ~ 2000

n

nin

i

i

qBnnkT

qBnP

BE

)exp()(11* 2

Reynolds number of ion-neutral friction

19

,~

nn

Turbulence diffusion coefficient

20

eiei nxn ,, )( eiteitei nnxn ,,, )(

eiei nn ,, eieitei nnn ,,,

eiteieitei

eieiteieiei

nxnnnnnnnn

,,,,

,2

,,,,

)(

eitteieiteitei

eieiteieieitei

nxnnnnnnnnnn

,,,,,

,2

,,,,,

)(

x+λtx

[A]

n ≡ xn

[B]

[C]

,~

nn

< 0

► net movement of one cycle is : same result from L-R-L and R-L-R cycles► turbulence induced charge diffusion :

nt t

► ion and electron move toward boundary => diffusion► charge (ρ) moves toward core => dilution current => Saturation by JGCS

Turbulence induced diffusion

212121

eBkTD e22

BE~1

~ nBE

D t ~

ekT

E et 2~ ( : , )

e

e

e

t

nn

kTe ~~

2~~ t

t E

nt

nt

eBkTD e22

Turbulence induced diffusion coefficientby GCS theory

[TFR group, 1986]Boltzmann

relation

[NSTX , 2010]

2► proportional to : agreed by experiments

,~

nn

22

Reynolds number of ion-neutral collision

DJ GCSr( saturation condition : )

02

E,dtdJ

t

eBkTD e22

,*Re

iLi

ni

r

),1(n

ni

i

i

ni

Lii

GCSr n

neBkT

nP

eBBErenJ

EnnmB

inniii

22

02

)(4Re

turbulence induced counter-current( )

ambipolar E-field and diffusion:Ideal case

Equilibrium of radial current and Reynolds number

23

EnnmB

inniii

22

02

)(4Re

DJ GCSr

),1(n

ni

i

i

ni

Lii

GCSr n

neBkT

nP

eBBErenJ

eB

kTD e22

[Lee, PPCF 2009]

L/H transition of tokamaks

24

quasi-neutrality is not valid for most charge exchanges

- electric potential vanishes away out of Debye shielding : ( screening effect )

- electric potential is effective inside Debye shielding- when charge exchange rate is high enough

=> all space become field effective

1xD r 1xD r

D 343

ii

cx

ix nr

: radius in which one charge exchange occurs

in average

D

25

)50~5()(ln

2313137

31313221670

6534

e

ncxie

x

D

nenTT

r

many test charges in a Debye shielding

iicxix nr 3

34

343

ii

cx

ix nr

𝜏 𝜏

ion-ion collisions makeredistribution of ions and Debye shielding disappeared

𝜏𝜏

number of ions requiredto have one point chargon average among them

26

1000/12

220

cnmB A

iiip

np

polarization drift tieEtE 0)(

c

tE

me

e

pe

2

tE

qBm eiei

p

2

,,=> quasi-neutrality

c

when

But tEeniGCSi )( 0 xe r

2

2

2

20

x

D

e

x

ei rr

tE

me

tE

en

GCSii

GCS enJ ,dtdJ

02

E,

27

[K.C. Lee, JKPS (2013)]

parameters of typical plasmas in which violation of quasi-neutrality takes place

28

two common features of black aurora and tokamak edge : 1. strong E-field, 2. breaking into circular structure

TV image of black auroraECEI measurement on KSTAR ELMs

[Hallinan and Davis, Planet. Space Sci. 1970]arc distortions of black aurora by ExB

A future work:What is the role of strong Erfor the ELM triggering?

[J.H. Lee, PRL 2016]

29

Conclusions

1. Gyro-Center Shift current is induced by ion-neutral collisions

2. E-field formations in tokamaks, arc discharge , EEJ and black auroraare explained by GCS current

3. Original Bohm experiment is explained by and short circuit effect

4. turbulence-laminar transition by ion-neutral frictionL-H transition in tokamak

5. turbulence induced diffusion is analyzed

8. Criterion of quasi-neutrality validity for charge exchange is discussed

GCSrJ