i:i-:iir' a b d u s s a l a meducational, scientificand cultural

organization

the

international centre for theoretical physics

international atomicenergy agency

SMR 1331/25

AUTUMN COLLEGE ON PLASMA PHYSICS

8 October - 2 November 2001

The a-effect and Current Drive Using Electron Bernstein Waves in the RFP

Cary Forest

Dept. of Physics, University of Wisconsin, U.S.A.

These are preliminary lecture notes, intended only for distribution to participants.strada costiera, 11 - 34014 trieste italy- tel. +39 040 22401 I I fax +39 040 224163 - sci_info@ictp.trieste.it - www.ictp.trieste.it

Outline

The a effect in the RFP-components of dynamo physicsRF heating and current in an RFP- Impact of current profile modification on performance- Magnetic geometry and dielectric properties

Electron Bernstein Waves- Propagation, absorption and current drive- Coupling

Emission measurements- Black body levels of emission observed

Coupling measurements- Agreement with waveguide coupling theory

Plans

The a effect in the Reversed Field Pinch

The a-effect predicted from mean-field electrodynamicsplays an important role in the RFP- Predicts generation of current in direction of pre-existing

magnetic field from fluctuations

Global kink-tearing modes provide fluctuating magneticand velocity fields (driven by gradients in currentdensity)

a effect generate toroidal magnetic flux from poloidalmagnetic fieldNot a dynamo since free energy source is gradients inmagnetic field energy- Referred to as "RFP dynamo-effect"

The standard RFP current profile is sustained by atoroidal electric field and MHD fluctuation driven currents

toroidal electric field drives toroidal current in core

peaked current profile is unstable to tearing modesConducting Shell

Surrounding Plasma

\

BT Small & Reversed at Edge

Tearing modes drive poloidal current in the edge andsuppress current in core

broad spectrum of tearingmode are driven by gradientsin X = JI I /B

core resonant m=0m=1 tearing modes modes

q(r) typical island width

magnetic stochasticity

current profile driven by MHDtowards a marginally stablecurrent profile (flat X)Island overlap causes Measured n.spectrumstochastic magnetic transport 1.5in core

0.5

0

i I I I I

Bin)B

mi

i ! I ! I

MST

I l l l i1 3 5 7 9 11 13

n

An cc-effect is needed to sustain the RFP equilibrium(Cowling's theorem applied to the RFP)

Assume axisymmetry and a simple Ohm's law (J = crE). Now considercurrent at reversal surface (surface where B^ = 0)

but

Je

dt

1 II

1<

oB4

w,

a1

o,

2nr

dr

thus no steady-state field reversal is compatable with simple Ohm's law.

An a-effect is needed to sustain the RFP equilibrium(continued)

Now consider an Ohm's law of the form (J = <TE +Now,

= -E027rrat

a>BA

OrNow, steady state is possible if

or(Recall Taylor state V x B = AB)

Toroidal flux for RFP equilibrium is periodicallyregenerated in discrete sawteeth events

Discrete Dynamo Events

10 20 30Time (msec)

40 50

Reversed field equilibrium can be sustained for manyresistive diffusion timesToroidal flux follows current

Theory of relaxation is beyond scope of this talk, but itinvolves

8

Velocity and magnetic field fluctuations can be measuredto estimate motional EMF from tearing modes

-1.5 -1.0 -0.5 0 +0.5 +1.0 +1.5Time relative to flux jump" (msec)

-1.0 -0.5 0 +0.5 +1.0Time relative to flux jump (msec)

+1.5

Mean-field EMF from tearing modes regenerate toroidalflux

1.0 -0.5 0.0 +0.5 +1.0Time relative to flux jump (msec)

+1.5

10

Hypothesis:

The RFP's poor confinement is a result of themisalignment of inductive CD profile and tearing modestable current profiles.

By non-inductively sustaining a current profile which islinearly stable to all tearing modes, the confinement inthe RFP will improve.

Produce a non-inductively driven Taylor-State

11

MHD simulations indicate partial current drive in the edgeregion of the RFP can reduce magnetic fluctuations

B2

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

-0.5

n e

with J( r)-control

StandardRFP

ad hocforce

profile

i I i I i

0. .2 .4 .6 .8 1.0rM

Nonlinear, 3D resistiveMHD computation

log

'~\2D

-2

-4

-6

-8

-10

; fir f;V' \\*/'. O>

,£: cc

: ?o

: IF• s s

Standard \RFP j

( \ ;

with \r '.Mr)-control •

-20 -10 0n

10

12

Current drive can heal flux surfaces

6p

StochasticField

Standard RFP RFP with Jdj-Control6p

Closed FluxSurfaces

0.00.0

v t

i •

II/ ; 1

)t^l

• f . \?::tK S-.

)•£'?'':".'"(•

>-4% \ i •

0.5 ij

13

PPCD: inductive electric field programming resultsreduction of magnetic fluctuations (for 10 ms)

Pulsed PoloidalCurrent Drive

4

E 2

i o

-4

C/5

0)

05

10

05

| 7

co 5

? 310

PPCD

1

" SXR

- density

t i l l

Ee(a) E|,(a) ^ ~

^ applied inductive JE,;>(a) ^ electric field

m=0 fluctuations

m=1 fluctuations^ (rms; ^ = 6 - 1 5 ) * ^ ^

8 10 12 14 16time (ms)

18 20

14

Electron energy transport is improved during PPCD:excellent target plasmas for RF current drive

Electron "Temperature

00.0 0.1 0.2 0.3 0.4 0.

p(m)

100Qtransport coefficients

100-

o.o d ' i 6 . 2 as A o-4f 0.5r ( m ) q=0 q=0

• %e t ' r o P s

PPCD

-T;E=10 ms, ne

P<1MW

1 0 during

= 0.5-1.0 x 1013 cm3

15

PPCD shows good fast electron confinement: runawayelectrons are present

80

60

40

20

Pulse height analysis of PPCD plasmas show 100 keV electrons

RF generated tail of the electron distribution function can be confined!

Fokker-Planck Modeling shows diffusion coefficient of 5m2/s, measured Zeff

matches data well, even with Diffusion=0m2/s, Zeff -3 needed

10~2msi5 20time (ms)

io-3

10-4

10-5

_

\

\

\\

-

-

-

' I '

/

,/••"

1 1 1

PPCD flux1

"».

I 1

1

at

re-

time

I

L <

ofMSTFit1 | . 1

II ,

—̂̂^̂ <><J

> • —

7sxr_./sxr

<

-—:

1 •

diff5"diff5

<>

* —

<

1 ,

_

-

z2.datz4.5.dat

-

-

<

:

> _

20 40 60Photon Energy (KeV)

80 100

16

MST plasmas are over-dense

High dielectric constant

> 5ce

Conventionalelectromagnetic waves inthe electron cyclotronrange of frequencies donot propagateLH wave accessibility islimited

40

N 3 0 L

CD

CD

20 L

1 0 L

0

lp = 300 kAmp, Ne = 10 13 em "3

0.0 0.1 0.2 0.3 0.4 0.5

r(m)

17

What type of waves might propagate for these parametersin the ECRF

Qi = &

Core plasmain low fielddevices forG>~2coce

0 Usual ECregime for to~2coce

18

The EBW propagates when the plasma is overdense

Hot plasma wave

Wavelength of order pe

Propagates nearlyperpendicular to magnetic fieldPrimarily electrostatic

8s

Typical EBW Dispersion Curves

Maxwellian *

Hot plasma dispersion can be evaluated numerically

Assuming a maxwellian distribution function f(v) =the hot plasma dielectric tensor is

oo / %InAn -in (In - I'n) An

K = 1 + Xe~x ]Tn——oo

in (In - I'n) An (?fln + 2A (/„ - I'n)) An

I -%N±InBn/Y -iN±(In-I'n)Bn/Y

K* K* \ / v ft {i) f~*\ /-v f\ 1 r

\A/hpm \ — -L — ±^ V — Pe \S — ^^ Q^ — ^ ^ J

VV1 IV-̂ I \^ /\ C^O —

the functions2Y'2' " w 2 f '

/ m \\27rfcT/

tATj. (/„o(l—ny)^" iVii/32

2. NL

3/2

- / ;J n B n

_ k

cxp 2kT ,

) s n /y

( i )

Bn — -

1 - nY

/ n = /n(A) is the modified bessel function, and Z(£) is the plasmadispersion function.

T.H. Stix Waves in Plasmas, AIP (1992) >o

Hot plasma dispersion (continued)

Solve wave equation

which in matrix form is

N X (N X E) + K . E = 0,

Kxy

^yx

\ Kzy

KXz

Kyz

Kzz -Nl j

Ex\Ey = 0,

Functionally, this is specified as

- N? K.xy

^yx

K zy

Kxz +Kyz

Kzz - Nl

(1)

(2)

(3)

Solve for ATj_, given X, Y, (3 and Nn. Dispersion found from ReD(N±r) = 0, whereiVj_jr is the real part of N; damping found from

(4)

21

Ray Tracing in general toroidal geometry

Once root is found, it can be followed with Hamiltonian ray tracing equations to solvefor the ray trajectories of the waves:

dz _ c dD/dNz dNz _ c dD/dz m

dr _ c dD/dNr m dNr _ c dD/dr .~ u dD/duj ' df ~

d<f> c dD/dm dm c dD/d<fi

tudD/du' dt ~The spatial derivatives are computed from equilibrium quantites and chain rule, ie.

3D _ dDdX 8DdY dDd(3

"57 ~ dX 3r dY dr ~d(3~drdD _ dDdX dDdY dDd/3

~dz ~ dX dz dY dz ~d/3~dz

= o

Toroidal equilibrium is used for calculation of magnetic field.

22

Numerical study of EBW propagation and absorption hasbeen carried out using GENRAY and CQL3D

Full hot, non-relativistic dispersion solver

Absorption is complete (nearly infinite optical thickness)

(a) Poloidal View

Forest, Chattopadhyay, Harvey and Smirnov,Phys. Plasmas 7, 1352 (2000) 0.0 0.1 0.2 0.3. 0.4

minor radius (m)0.5

23

N|, up-shift and direction of CD can be controlled byi i d i l h i ipoioidai launch position

0.2 0.3minor radius (m)

0.4 0.5

24

RFP physics is similar to ST physics(ECH characteristics of Pegasus are similar to MST)

(a) poloidal view

0.2 0.4 0.6 0.8minor radius (r/a)

1.0

/Vdriven current densitytotal = 39.5 kApower = 100 kWne(Q)=1019rrf3

Te(0)=1 keV

\

0.2 0.4 0.6minor radius (r/a)

0.8

Forest and Ono, Bulk Am. Phys. Soc. 35, 2057 (1990)Forest, Chattopadhyay, Harvey and Smirnov, Phys. Plasmas 7, 1352 (2000)

25

Current drive is computed from solution of Fokker-PlanckEquation (CQL3D)

Hot plasma dispersion is non- 1relativistic

CQL3D uses non-relativisticpolarizations but fully relativisticFokker-Plank treatment

Wave diffusion determined fromelectric field (from ray tracingcode) o

1

contours of quasi-linear diffusion

U||/Uo,

1

26

History of Coupling

Early theory- Mode conversion theory Stix (Phys. Rev. Lett, 1966)

• Couple to the EBW using an X mode launched from the high field side- Hot plasma waves (Bernstein)

Early experiments (-1970)- Observation of the EBW (Leuterer, Stenzel, Armstrong)- Non-linear effects and heating (Porkolab)

OXB mode conversion identified (1972)- Pioneering work by Preinhalter and Kopecky, 1972- Later work by Batchelor and Goldfinger

Tunneling through XB (Sugai)Demonstration of OXB on Wendelstein 7-AS- Heating, emission (Laqua, et al 1996, 1998)

Recognized as possible heating source for STs- Forest (1990), Ram and Bers (1998)

Ongoing research on STs and RFPs

27

X-mode incident on upper-hybrid resonance from highfield or high density side smoothly mode converts into

EBW: classic mode-conversion problem

.1 R =

"Fast"X-Mode

increasingdensity or B

T.H. Stix, Phys. Rev. Lett. 15 878 (1965)

28

Launching the EBW with high field side X mode for insidelaunch 60 GHz ECH on Dlll-D

Top View

4

3

i.00.0

density

0.2 0.4 0.6 0.8 1.0rho

29

EBW may play a role in understanding the "Heat-Pinchresults on Dlll-D

CD

CD un

EO> en

0>

oQ_

C\l

power deposition

EBW

/ \ first pass/ V X-mode

0.0 0.2 0.4 0.6rho

0.8 1.0

C.B. Forest, R.W. Harvey, A.P. Smirnov, Nucl.Fusion 41 619 (2001)

111

0.2 0.4 0.6

rho1.0

30

Constructive interference between right and left handcutoffs can result in efficient mode conversion

Plasma cutoffs at

/L = 2

/ft — 2

/ce +

/c2e +

4 /2pe

1 - AT,

1/2 \

2 | ~h /ce

/

4 / 2

1-AT,

1/2

ce

The cold plasma resonance at fuh = yjff%, + .couples the x-mode and EBW when hotplasma effects are considered.

Cutoff-resonance-cutoff triplet can give 100percent mode conversion:

Cmax —

1 (u>peL

a \n

uh1 + a1 - 1

ai ~~

Ram and Schulz, Phys. Plasmas 7 p. 00(2001)

1.0

w 0.8

E 0.603

Hc

NX

0

EBW

slow x-mode

cold plasmadispersionat 3.6 GHz

fast x -mode

0.47 0.48 0.49 . . 0.50r (m)

0.51 0.52

acuum= 9 cm

31

Full-wave calculations validate mode conversion processand predict surface impedance for coupling calculation

M

0

+

wo4

047

1: 1 1 i | I 1

juAAV1

ft I

i , * )

IBI =f =Te =

i i t

i i | i t _

0.08 T :

3.6 GHz "50 eV

-

i i i . , "

0.48 0.49 0.50minor radius (m)

0.51

Simulations using GLOSI code, M. Carter ORNL

32

Impedance match depends upon density scale length andangle of incidence perpendicular launch

0,0 0.2 0,5 0.8 1.0transmission forX mode incident

1,-0.25 cm L= =0.5 cm

Shallowest gradient

r » 3 mm

r >> 0.05 mm

Transmission depends on perpendicular wavenumber (n )̂ ofincident waveCalculations done for a plane wave incident from vacuum

33

Phased array of waveguides can be used to match toEBW

E l

E l

tBo

yA

Nf

Matching Ey at x = O_|_and Bz in waveguide opening determines powercoupled to plasma. For one waveguide

1 - P A koa= A =+r sin2 (/ dnvY(n<u) ^

~2T'ly

(i)

where Y(ny) =x=0

is determined from plasma physics. Has beengeneralized to multiple waveguides.

[M. Brambilla, Nucl. Fusion 16 47 (1976)] 34

Reflected power depends upon phase betweenwaveguide, consistent with freespace picture

80

70

50

40

30

20

10

0

CDOO

§o

2CD

ba.

3.4 GHz, pair of7.21 X 3.45 cmwaveguides

Vacuum case

Plasma case

-180 -135 -90 -45 0 45 90 135 180

Phase angle between waveguides (deg)35

Ordinary-Extraordinary-Bernstein Mode is also possible

Coupled Power Fraction

X-mode O mode

K0.00 0.25 0.50 0.75 1.00

36

3.7-8 GHz radiometer has been constructed andabsolutely calibrated

16 Channel Radiometer schematic

16channeHir*l....l6)Central freq, - 4 * (n-l )*0.25 GI fz3 dB bandwidth - 125 MHz

Antenna DC block Amplifier Attenuator AnipIifierAttenuator

Antenna Specification

Bandwith: 3.8-8.4 GHzPolarization: LinearDirectivity: 13-17 dBLocation: 15 deg poloidal from horizontal mid planeAntenna looks at either O or X mode polarization.An II = 0.5

ilandpass E lec to r Video OutpiFitter Amplifier

37

Emission correlates with MHD activity

300

Q- 200 :

100 L

CO

E

oT"™

8

6

4

2

- o . TO

- 0 . 2 0 •"

-0.30 r

-0.40 r

0

300

> 200(D

l ioo

> 200

2 ioo

0

M, 200

100

10 20 30 40 50time (ms)

Ch7=5.5 GHz

Gh11=6.5GH;

0 10 20 30 40 50time (ms) 33

Black-body levels of electron cyclotronemission are observed

250

-. 200 :

£ 150^

SI 00500

• 1st

-

; x *• i i

harmonic

4

ill'. 1 . . .

i ' 2nd1|

li-armfonfc1 ' ' \

$ x mode

f o mode

-

, s * - m *. x * * :j i . . • • i • • • i i

0.2

5 6f (GHz)

8

250200

> 150

^ 1 0 0

500

^~~i*4s1 st harmonic

1 K i \

: , X,

2nd harmonic :* Thomson$ x mode| o mode

-

1* :

* 4 « **:-• i i i i i •

0,3 0.4minor radius (m)

0.5

flux surfaces

harmonicloverlap• i • • 1 1 1 1 • 1 1 1 1 1 • 1 1 1 • 1 1 1 1 1 1 1 1 1 1 1 1 1 • • 1 1 1 • • 1 1 1 1 1 • 1 1 • 1 1 1 1 1

5.5 GHz ray

0.00 0.10 0.20 0.30 0.40minor radius (m)

0.50

39

Comparison with coupling theory is underway butcomplicated by wall reflections

Maximum XB modeconversion efficiency

(

Horn antennna

v = -a uh

1 + a2 -

a =COpe

-ce

Applying balance of incomingradiation

T T -*-xbbbl-(l-Txb)R

„, _ (1-R)C „_ I1-RC ' hb

Reflectivity depends uponangle of incidence

^0.4

S 0.2

mode conversionlayer

40

Active coupling studies are underway using singlewaveguide and double waveguide array

Reflectometry SchematicRF- source

Bidirectional coupler(22dBcoup,28dBclr)

Isolator

dB IFor Power

ower splitter Power Splitter

Amp Video Det.

Hybrid CouplerCP 9GP

Lim. amp\V

Mixer'

TWT(10W)24GHz

RefPov^r

Video Det.

Low PassFilter

LowPassFilter

T TCos(f) Sin(f)

LevelingLoop

Video Det.

41

PPCD plasma presents low reflection

1.0

0.6

0.21.0

0.6

0.2

^ 2 . 0

51.0

o8

9 4

z * o 1

Forward Power

Reflected Power

Edge ElectronCyclotron Frequency

Edge Density"

10 20Time (ms)

30

LL

o

200

100

01

0

-1

-2

1.5

1.0

C 0.5

0.8

ffl 0.4

0.0

PlasmaCurrent

Line Average Density -

Reflection Coefficient -

10 20

Time (ms)30

42

Reflection varies with frequency in accord with theory

3.2 3.4 3.6 3.8Frequency (GHz)

o

4.0

0.8

0.7

0.6

0.5

0.3

0.2

0.1

0 ,

PPCD like conditionssingle waveguide

A A AA A

A phase shift

O Power reflection coeff.o

° o o o o o

80

60

40

620

2.5 3 3.5f (GHz)

43

Plans for EBW

Antenna development and edge conditioning to furtheroptimize couplingDemonstrate heating- TWT: 3.6 GHz, 5 ms, <200 kW- Measure power deposition (HXR)

Wave physics- Does power get to cyclotron layer in this over-dense plasma?- Measure EBW in plasma (probes or CO2 scattering experiment)- Test off-mid-plane launch CD scenario

• N|| up-shift and hence, Doppler shifted resonance location, isdifferent for above and below mid-plane launch (power depositionor emission region differs)

44