Download - Alpha Particle Transport Induced by Alfvénic Instabilities in Proposed Burning Plasma Scenarios

G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 2003 1

Alpha Particle Transport Inducedby Alfvénic Instabilities inProposed Burning Plasma

ScenariosG. Vlad, S. Briguglio, G. Fogaccia and F. Zonca

Associazione Euratom-ENEA sulla Fusione, C.R. FrascatiC.P. 65 - I-00044 - Frascati, Rome, Italy


Outline• Introduction• The numerical model• Nonlinear Energetic Particle Modes (EPMs) dynamics: avalanches• Burning-plasma devices/scenarios• Comparison of different devices/scenarios:

– linear stability– nonlinear energetic particle transport

• Check of the model• Preliminary results on ITER-FEAT Hybrid scenario and

comparison with ITER-FEAT Standard and Reversed Shear ones• Conclusions


Introduction• Particle simulations have shown that transport and confinement

properties of energetic ions in Tokamak plasmas can besignificantly affected by shear Alfvén modes driven unstable bypressure gradients of the energetic ions themselves

• Scenarios for proposed burning-plasma experiments (ITER-FEAT,IGNITOR, FIRE) include alpha-particle b profiles, which do nottake into account the effects of shear Alfvén modes

• Aim of this paper is investigating the consistency of some of thesescenarios with shear Alfvén mode-particle interactions:a) stability of shear Alfvén modes (Energetic Particle Modes,

EPMs)b) effects of unstable modes on alpha-particle profiles and

confinement• The investigation is performed by particle-in-cell simulations

(HMGC code)


The numerical model-1• The Hybrid MHD-Gyrokinetic simulation Code (HMGC) solves

the set of reduced O(e3) MHD equations, coupled with fullynonlinear gyrokinetic Vlasov equation for energetic (“Hot”)particles

• Relevant equilibrium profiles retained: q, ni, bH/bH0 (we keep bH0as a free parameter)

• Large aspect ratio approximation (most of simulations presentedrefer to R0/a=10.): bH0 rescaled to yield the desired value ofaH≡R0q2b'H

• Circular shifted magnetic surfaces• Single toroidal mode number dynamics: nonlinear mode-mode

coupling among different toroidal mode numbers neglected (scanin n to find most unstable mode)


The numerical model-2• Isotropic Maxwellian (instead of slowing-down) energetic-particle distribution function• Particles are loaded initially in (m, V||, y) space, and not in (pf, E, m) space (initial

relaxation of assigned radial EP profile are observed).• Shear-Alfvén equivalence between simulation (Maxwellian) distribution function and

physical one (slowing-down)• match respective energetic-particle response:

– Maxwellian (Maxw): ~aH,MaxwVth,HdWMaxw(w/k||Vth,H)– Slowing-down (SD): ~aH,SDVSDdWSD(w/k||VSD),

with VSD≡(2Efus/mH)1/2

• Matching the dominant energetic-particleresonance:

Vth,H @ 0.37VSD

• Matching the drive intensity:aH,SDVSD @ 1.606aH,MaxwVth,H

• fi aH,Maxw @ 1.683aH,SD


frequency(r/a,w/wA)

Energetic particlebH(r)

differential local drivedaH=aH(r,t)-aH,lin(r)

eigenfunctionfm,n(r)

Nonlinear EPM dynamics: overview (strongly unstable RS equilibrium)


Burning-plasma devices/scenarios

0

1

2

3

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0r/a

q

H/

H0

H/

Hmax

ni/n

i0(a)

0

1

2

3

4

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0r/a

q

H/

H0

H/

Hmax

ni/n

i0(e)

0

1

2

3

4

5

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0r/a

q

H/

H0

H/

Hmax

ni/n

i0(b)

0

1

2

3

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0r/a

q

H/

H0

H/

Hmax

ni/n

i0

(d)

0

1

2

3

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0r/a

q

H/

H0

H/

Hmax

ni/n

i0(c)

ITER-FEAT IGNITOR FIREm

onotonic q(from

Budny, Nucl. Fusio n

4 2 (2 002 ) 1 383 )

Re ver se d She ar


Toroidal gap structureITER-FEAT IGNITOR FIRE

monotonic q

Reverse d She ar

Alfvén continuumin (r/a,w/wA) space(wA≡VA/R0) for n=4


Results• Are the proposed scenarios stable w.r.t. shear-Alfvén modes?• If unstable, which consequences for alpha-particle confinement?

fi Are the proposed scenarios consistent with Alfvén modesdynamics?

• In order to compare different devices/scenarios we normalize thefree simulation parameter bH0 to the “scenario” value bH0,scenario.


Results: linear stability-1ITER-FEAT IGNITOR FIRE

monotonic q

Reverse d She ar

n=4 mode

bH0 above thresholdfor EPM instability


• The n dependence of the real frequency is slightly weaker than linear• Linear dependence would suggest precession resonance to be the relevant one:

wprecession µ nq(r)/r• For small n, mode could locate itself in a “valley” of the Alfvén continuum

Toroidal mode number n dependence of toroidal gapstructure and real frequency (ITER-FEAT RS)

Results: linear stability-2

0

0.1

0.2

0.3

2 4 6 8n

wgap/wA=1/[2q(r)]

wlin/wA


Results: linear stability-3

• bH0,Th≡ threshold in centralenergetic particle pressure bH0(for fixed profiles and otherparameters) for destabilization ofresonant EPMs

• All the considered scenarios arestable w.r.t. EPMs,(bH0,Th >> bH0,scenario),with the exception of theReversed Shear ITER-FEATscenario. 0

0.1

0.2

0.3

0.4

0.5

1 10

glin/wA

bH0/bH0,scenario

ITER-FEAT RS n=2

ITER-FEAT n=8

FIRE n=4

IGNITOR-RS n=4

IGNITOR n=4


Results: nonlinear effects on a confinement-1• ITER-FEAT RS scenario, n=2 (unstable at nominal bH0)• Power spectra in the plane (r,w) and bH profiles (bH0/bH0,[email protected])

Linear After avalanche Fully saturated


0.50

0.60

0.70

0.80

0.90

0 50 100 150 200 250 300

rmax

t/tA

0.03

0.04

0.05

0.06

0 50 100 150 200 250 300

[d(rnH)/dr]

max

t/tA

linearphase

convectivephase

diffusivephase

Results: nonlinear effects on a confinement-2

Linear phase

rnH

rmax

0.5 0.6 0.7 0.8 r

rmax

rnH

0.5 0.6 0.7 0.8 r

Convective phase

rnH

0.5 0.6 0.7 0.8 r

Diffusive phase

rmax

Convective phase (avalanche): maximum gradient of rnH shifts outward, first steepeningand then relaxing


0.0 0.2 0.4 0.6 0.8 1.0

rbH

r/a

y=85%

(r/a)85%

Results: nonlinear effects on a confinement-3• Saturation of EPMs takes place via an avalanche mechanism, which produces a

macroscopic convective redistribution of the energetic-particle source• After the convective displacement has completed, a significant diffusion of

energetic particles survives because of the continuous scattering of the energeticparticles in the saturated electromagnetic fields

• Define (r/a)y: the radial position of the surface containing a fraction y of thealpha-particle energy:

†

y =xbH (x;t)dx

0

(r /a )yÚxbH ( x;trelax )dx

0

1Ú

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0 50 100 150 200 250 300

(r/a)y

t/tA

(r/a)95%

(r/a)90%

(r/a)85%

linearphase convective

phase

diffusivephase

~trelax


Results: nonlinear effects on a confinement-4• Both convection and diffusion are more pronounced for larger bH0 (larger

saturated field levels)• Characterize the convection with r/a85% at the end of the convection phase• Characterize diffusion by tdiff,95%≡(r/a)95% [∂(r/a)95%/∂t]-1 (tdiff,95%

-1µD)

10-5

10-4

10-3

10-2

1 10

tA/tdiff,95%

bH0/bH0,scenario

ITER-FEAT RS n=2

ITER-FEAT n=8

FIRE n=4

IGNITOR-RS n=4

IGNITOR n=4

0.3

0.4

0.5

0.6

0.7

0.8

1 10

r/a85%

bH0/bH0,scenario

ITER-FEAT RS n=2

ITER-FEAT n=8

FIRE n=4

IGNITOR-RS n=4

IGNITOR n=4


0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6

g/wA

bH0/bH0,scenario

R0/a=3.3

R0/a=10.

Check of the model (ITER-FEAT RS)• Large aspect ratio approximation:

a) (R0/a)sim = 10. ‹fi (R0/a)[email protected]) Rescaling bH0 to keep local drive (aH)

constant:bH0,sim (R0/a)sim = (R0/a)ITER-FEAT bH0,ITER-FEAT

• Is a) + b) equivalent to take realconfiguration:bH0,sim = bH0,ITER-FEAT

(R0/a)sim = (R0/a)ITER-FEAT ?

R0/[email protected]

R0/a=10


ITER-FEAT Hybrid scenario-1• No transport code generated scenario available. Use a

simple model:– parabolic bulk temperature profiles (T@20KeV)– bulk plasma density profiles as for standard

ITER-FEAT scenario (n@1¥1020m-3)– alpha particle profile from fusion reaction rate

(Peres) and slowing down time– safety factor: [email protected], [email protected] (q95%@4.1) with

almost zero shear up to [email protected]

1

2

3

4

5

6

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1r/a

q

bH

/bH0

aH

/aHmax

ni/n

i0

Te/T

e0

n=12n=4 n=8


ITER-FEAT Hybrid scenario-2

• Comparison between Hybrid scenario and Standard andReversed Shear ones: linear unstable modes.

Hybridmost unstable mode: n=8

Standardmost unstable mode: n=8

Reversed Shearmost unstable mode: n=2


ITER-FEAT Hybrid scenario-3• Linear growth rates and radial position of the surface containing y=85% of the alpha

particle energy of the three ITER-FEAT scenarios considered (most unstable n)• Compare the different scenarios w.r.t. the absolute central energetic particle bH0 (for

the Hybrid one, no reference value is available!)• Hybrid scenario looks to be promising:

– higher bH0,Th

– it supports (in a limited range of bH0) a saturated EPM without displacingappreciably the energetic particle profile: bH0,Th-avalanche > bH0,Th

ITER-FEAT HybridbH0,Th

ITER-FEATbH0,scenario

ITER-FEAT RSbH0,scenario

ITER-FEAT HybridbH0,Th-avalanche

0

0.1

0.2

0.3

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

glin/wA

bH0

ITER-Hybrid-n8

ITER-RS-n2ITER-n8

0.55

0.6

0.65

0.7

0.75

0.8

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

r/a85%

bH0

ITER-Hybrid-n8ITER-RS-n2

ITER-n8


Conclusions• Shear Alfvén dynamics and interactions with energetic particles

must be retained in order to determine self-consistent fusion-product profiles for the reference scenario

• The Reversed Shear ITER-FEAT proposed scenario, in particular,appears to be unstable w.r.t. Energetic Particle Modes

• These modes are able to broaden alpha-particle profiles both viaconvective (avalanche) and diffusive mechanisms

• Small increase of the alpha-particle energy content (w.r.t. thereference scenario) could produce large thermal loads on the firstwall

• Needs for a “transport generated” ITER-FEAT Hybrid scenario• Future work: general equilibrium code (in progress)


Fine presentazione


Most unstable toroidal mode number (ITER-FEAT RS)• The n dependence of the real

frequency is slightly weaker thanlinear

• fi linear dependence wouldsuggest precession resonance to bethe relevant one: wprecession µ nq(r)/r

0

0.05

0.1

0.15

0.2

0.25

0 0.005 0.01 0.015 0.02 0.025

lin/ A

H0

n=2n=4n=8

n=8

n=4

n=2

0

0.1

0.2

0.3

2 4 6 8n

wgap/wA=1/[2q(r)]

wlin/wA

The n=2 linear mode grows in a “valley” of the Alfvén continuum:it suffers less damping and it is more effective in displacing particles.

0.55

0.60

0.65

0.70

0 0.005 0.01 0.015 0.02 0.025

r/a85%

bH0

n=2

n=4n=8


Most unstable n

0

0.05

0.1

0.15

0.2

0.25

0.3

0 2 4 6 8 10 12

all-devides-w-real-gam#28E6

gamma-lin/w-A-ITER-SC4gamma-lin/w-A-ITER-Budnygamma-lin/w-A-IGNITOR-RSgamma-lin/w-A-IGNITOR-Budnygamma-lin/w-A-FIRE-Budnygamma-lin/w-A-ITER-Hybrid-1

glin/wA

n

Fixed bH0 (differentvalue for differentdevices/scenarios)