physics and control of fast particle modes

Hefei, China/ August 2012 / 2nd Lecture Valentin Igochine1

Physics and control of fast particle modes

Valentin Igochine

Max-Planck Institut für PlasmaphysikEURATOM-Association

D-85748 Garching bei München Germany


Outline

• Motivation • Physics of Fast Particles

• Fast particles in tokamak• Alfven waves• Influence of the geometry and kinetic effects• Different types of modes

• Control and active study of fast particle modes• Excitation of the modes by fast particle• Possibilities for control of fast particle modes

• Summary


Redistribution / Loss of Fast Particles

• Loss of bulk plasma heating

– Unacceptable for an efficient power plant

– May lead to ignition problems

• Damage to first wall

– Can only tolerate

fast ion losses of a

few % in a reactor


Toroidal direction

Ion gyro-motion

Fast ion trajectory

Poloidal directio

n

Projection of poloidally trapped

ion trajectory

Fast Ion Orbits

Various natural frequencies associated with particle motion

ωφ

ωθ

ωci


Burning Plasmas

• New physics element in burning plasmas:– Plasma is self-heated by fusion alpha particles

vTi << vA < vα << vTe

vTi = 0.9106 m/svA = 8106 m/s

vα = 12106 m/svTe = 59106 m/s

ITER parameters

++

+Deuterium

+TritiumEnergy

++

Helium

Neutron


Alfvén waves and αs

Alfvén wave is very weakly damped by background

plasmaα3.5 MeV

e

10 keV

i10 keV

Fusion products (αs) interact with Alfvén waves much

better than thermal plasma


Ideal MHD, linearized force balance

Boyd, Sanderson, The Physics of Plasma

Alfvén waves


Alfvén waves

Incompressible. Produce neither density nor pressure fluctuations.This mode is usually driven unstable by geometrical effects or finite current

Perpendicular plasma kinetic energy (i.e. inertial effects)

Line bending magnetic energy (i.e. field line tension)


Alfvén waves

fast magnetosonic (compression Alfven)

slow magnetosonic (sound wave)

All three solutions are real and the waves propagate without growth or decay. There is neither dissipation to cause decay nor free energy (currents) to drive instabilities.


r

r

20

Alfvén waves in cylinder

No wave packet of finite size across the magnetic field can persist for a long time since each slice moves with different velocity and in a different direction (phase mixing)


Alfvén waves in cylinder

No wave packet of finite size across the magnetic field can persist for a long time since each slice moves with different velocity and in a different direction (phase mixing)

Kinetic effects modify the dispersion relation

reduced kinetic limit: mode conversion to the kinetic Alfven wave (mode conversion)Result: Modes are strongly damped!

P.Lauber LIGKA results


Alfvén waves in torus

Cylinder Torus




Cylinder Torus

Toroidal geometry removes the crossing points of two neighboring continuum branches (m and m+1) and generates gaps

The global modes are only weakly damped by Landay damping within the gaps. No continuum damping! P.Lauber LIGKA results


Alfvén waves in tokamak


Toroidal Alfven Eigenmodes (m, m+1)

Ellipticity induced Alfven Eigenmodes (m, m+2)

Non-up-down-symmetric Alfven Eigenmodes (m, m+3)

Kinetic TAEs: two kinetic alfven waves that propagate towards each other and form a standing wave between two continuum intersections at a given frequency


Fast Particle Modes as they are seen by diagnostics

Temperature perturbations due to fast particle modes [P. Piovesan, V. Igochine

et.al., NF, 2008]

fast ions

//vvvtot


Alfvén cascades

JET

Cascades

The mode is highly localized


Alfvén Cascades

• Reversed magnetic shear scenarios have an off-axis extremum in the magnetic helicity– New type of AE associated with point of zero magnetic shear

0

0

0

-8 -6 -4 -2 0 2 4 6 8

0

x

11

(x) 12

(x)

q0

=2.920

q0

=2.875

q0

=2.860

q0

=2.850

AC

TAE qm

in d

ecr

easi

ng

in

tim

e

m=12Time evolution of n = 4 Alfvén continuum

qmin = 3.0, 2.9,…2.4 1, 2, ...7

Radius

Frequency

[v

A/R

0]

Radius

Mode s

truct

ure

,

m=11,12

B.N. Breizman et al., Phys. Plasmas 10 (2003) 3649


Diagnostic Potential

Fitting dispersion relation provides a powerful diagnostic for determining evolution of safety factor profile– Can be used monitor scenario development

Alfvén Grand

Cascade

AA vntq

m

Rvtkt

)(

1)()(

min0||

qm

inFr

equency

[kH

z]

Time [s]

MHD spectrosco

py

TAEs


New diagnostic capabilities for fast particle modes


Overview:modes that can be driven by energetic particles

toroidal mode number n

Fre

que

ncy

of t

he

mod

e

EPM, BAE

coupling between shear Alfven, acoustic, drift modes

Cascades (n=3-8)

TAEs, KTAEs, KAWs: shear Alfven,electromagneticJET(n=1,2...) AUG(n=4-7) ITER(n=7-12)


Excitation and control of fast particle modes


A simple picture for the interaction of fast particles with MHD modes

An effective interaction between a wave and particles is possible only in case of a resonance (vparticle ~ vwave), i.e. the particle always feels the same phase of the wave and thus constant force

In the frame moving with the wave (and the particle) an additional electric field occurs

BvE wave

* BvE wave

*

The electric field perturbation gives rise to an ExB drift:

22

*)(

B

BBv

B

BEv wave

r


Radial drift of particles due to wave-particle interaction

Br

vwave

. B

BrE*

vr

vwave

. B

BrE*

vr

22

*)(

B

BBv

B

BEv wave

r


Particles moving outwards loose energy

2 2 *|| 0

1( )

2p r

mE v v b e E

BR

Br

vwave

. B

BrE*

vr

vwave

. B

BrE*

vr

Ep>0

Ep<0

Particle gains energy during inward motion

Particle loses energy during outward motion

This drift motion corresponds to a change in the particle energy:

* /pE Zev E


Landau damping and fast particle modes

Energy exchange between a wave with phase velocity vph and particles in the plasma with velocity approximately equal to vph, which can interact strongly with the wave.

accelerated decelerated

wiki

During this process particle gains energy from the wave without collisions.

More slower particles


Landau damping and fast particle modes

Energy exchange between a wave with phase velocity vph and particles in the plasma with velocity approximately equal to vph, which can interact strongly with the wave.

accelerated decelerated

wiki

During this process particle gains energy from the wave without collisions.

But if the distribution function different the result could be opposite! Waves (instabilities) will gain energy from the fast particles. This produces fast particle driven mode.

More faster particles


Drive by fast particles only if resonance condition fulfilled

Particles always see the same phase if:

|12|||

l

vv A

primary resonance at never fulfilled on ASDEX Upgrade (only weak drive by NBI vNBI~vA/3)

Avv ||

For passing particles (TAE modes):

vAvA/2vA/3 3vA/5 Velocity

Dis

trib

uti

on

EAETAE

NAE TAE


Drive by fast particles only if resonance condition fulfilled

Particles always see the same phase if:

|12|||

l

vv A

primary resonance at never fulfilled on ASDEX Upgrade (only weak drive by NBI vNBI~vA/3)

Avv ||

For passing particles (TAE modes):

For trapped particles:

bounceprecTAE pn

Resonance with multiples of the bounce frequency possible

relevant for fishbones

relevant for TAEs(driven by ICRH)


fTAE

fmeas

dampB

Active Excitation Antenna

• Allows measurement of proximity to instability

• Drive stable AE and measure plasma response– AE damping rate

n=1 TAE damping vs. plasma shape

Triangularity Elipticity

JET TAEantenna

[D Testa et al.]

One of the main questions: How strong the mode is damped?


Effect of plasma shape

ITPA Energetic Particles Topical Group code-experiment comparison

– n = 3 TAE in JET

– Excellent agreement withfrequency & mode structure

[THW/P7-08, IAEA FEC (2010)]

Elongation scan

n = 3

#77788

But…this damping measurements sensitive to distance between vessel wall and plasma. (This should be done carefully.)


Close Alfvén frequency gaps!

• Engineer Alfvén continuum so gaps aren’t open!– Centre of frequency gap ~ vA/(2qR)

– So make q2n a strong function of radius

• How?– Current drive and fuelling (pellets)


Damping Mechanisms

• Continuum damping– Phase-mixing occurs where mode intersects continuum– Depends upon alignment of frequency gaps and thus

profiles: ωAE ~ vA/qR ~ 1/q√n

• Thermal ion Landau damping

– γd ~ q2 and depends upon βi

– For Tth,T = Tth,D, vth,T < vth,D, D provides stronger LD than T

• Radiative damping– FLR corrections lead to finite radial group velocity


Radius

Energy [MeV]

Fast Particle Drive

• Collective instabilities

– Fast particle gradients act as source of free energy

• Non-Maxwellian distribution

~ f/E - n f/

– Negative radial gradient

Drive (n>0)

– Negative energy gradient

Damping


Alphaparticles

Tailor Fast Particle Distribution?

• Alpha particles peaked on-axis• Use off-axis beams to change drive-damping

balance?

Radius

Dis

trib

utio

n F

unct

ion

NBI

df/dr < 0 strong

alpha drive df/dr > 0 strong

beam damping


Effect of β on existence of TAEIncreasing β

• Alfvén continuum in START– Modes move out of gap as

thermal pressure increases

CSCAS

[Gryaznevich & Sharapov, PPCF 46 (2004)]

No modes!


Overlap of the modes is a potential danger

While single toroidal Alfven eigenmodes (TAE) and Alfven cascades (AC) eject resonant fast ions in a convective process, an overlapping of AC and TAE spatial structures leads to a large fast-ion diffusion and loss.


Fast particle losses from core BAEs

•Non-Alfvenic character! •Driven by radial gradient of ICRH-heated ions•low-frequency gap in Alfven continuum induced by ion compressibilitym=4;n=4;5 mode follows dispersion relation(B-field dependence cancels)

BAE


Different mechanisms for particle losses

Linear dependence of the coherent losses at the TAE n=3 frequency on the MHD fluctuation amplitude

Quadratic dependence of the incoherent losses on the TAE n=5 fluctuation amplitude

M. Garcia-Munoz et al., EPS 2010

transient losses, due to resonant drift motion across the orbit-loss boundaries in the particle phase space of energetic particles which are born near those boundaries

diffusive losses above a stochastic threshold, due to energetic particle stochastic diffusion in phase space and eventually across the orbit-loss boundaries.


Different mechanisms for particle losses

Quadratic dependence of the incoherent losses on the TAE n=5 fluctuation amplitude

diffusive losses above a stochastic threshold, due to energetic particle stochastic diffusion in phase space and eventually across the orbit-loss boundaries.

Due to the large system size, mainly stochastic losses are expected to playa significant role in ITER.

Stochastic threshold

• single mode

• multiple modes


What should be done next?

Considered situation Real situation

mode

fastparticle

mode

background plasma(turbulence, flows, etc.)

fastparticle

+ nonlinear evolution of the system


Fast particle physics summary

• Alfven modes are typically strongly damped by continuum damping

• Toroidal geometry, ellipticity and other effects lead to gaps in the continuum where the modes are weakly damped

• Fast particle (gradients in energy and velocity space and gradient of the distribution function) could drive these modes to unstable regimes

• Big drive from fast particles could even overcome continuum damping (Energetic particle modes, EPM)

• Overlap of the modes leads to bigger particle losses. This could be a potential danger for future scenarios in ITER.


Fast particle control summary

• Affect stability/existence of Alfvén eigenmodes– Plasma conditions: density, safety factor, beta, isotope

mix (mass density), magnetic field, introduce flow (rotation)

• Tailor fast particle distribution to change drive– Alphas: Fuelling– NBI: Beam geometry, injection energy– ICRF: Resonance layer– Field topology: Ripple, 3D field coils,

aspect ratio• Avoid mode overlap if possible


Interesting papers

physics and control of fast particle modes

Documents