transition from weak to strong energetic ion transport in
TRANSCRIPT
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 1
Transition From Weak to Strong Energetic Ion Transport
in Burning Plasmas
F. Zonca 1), S. Briguglio 1), L. Chen 2), G. Fogaccia 1), G. Vlad 1)
1) Associazione Euratom-ENEA sulla Fusione, C.R. Frascati, C.P. 65 - 00044 - Frascati, Italy.
2) Department of Physics and Astronomy, University of California, Irvine, CA 92717-4575.
Vilamoura, Portugal, November 1–6 2004
20th IAEA Fusion Energy Conference
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 2
Background
2 A burning plasma is a self-organized system, where collective effects associ-ated with fast ions (MeV energies) and charged fusion products may altertheir confinement properties and even prevent the achievement of ignition.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 2
Background
2 A burning plasma is a self-organized system, where collective effects associ-ated with fast ions (MeV energies) and charged fusion products may altertheir confinement properties and even prevent the achievement of ignition.
2 Simulation results indicate that, above threshold for the onset of resonantEnergetic Particle Modes (EPM) (L. Chen, PoP 94), strong fast ion trans-port occurs in avalanches (IAEA 02).
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 3
Avalanches and NL EPM dynamics (IAEA 02)
|φm,n
(r)|
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.05
0.1
0.15
0.2
0.25
x 10-3
r/a
8, 4 9, 4
10, 411, 412, 413, 414, 415, 416, 4
- 4
- 2
0
2
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
δαH
r/a
= 60.00t/τA0
|φm,n
(r)|
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.05
0.1
0.15
0.2
0.25
x 10-2
r/a
8, 4 9, 4
10, 411, 412, 413, 414, 415, 416, 4
- 4
- 2
0
2
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
δαH
r/a
= 75.00t/τA0
|φm,n
(r)|
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
.001
.002
.003
.004
.005
.006
.007
.008
.009
r/a
8, 4 9, 410, 411, 412, 413, 414, 415, 416, 4
- 4
- 2
0
2
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
δαH
r/a
= 90.00t/τA0
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 2
Background
2 A burning plasma is a self-organized system, where collective effects associ-ated with fast ions (MeV energies) and charged fusion products may altertheir confinement properties and even prevent the achievement of ignition.
2 Simulation results indicate that, above threshold for the onset of resonantEnergetic Particle Modes (EPM) (L. Chen, PoP 94), strong fast ion trans-port occurs in avalanches (IAEA 02).
2 Such strong transport events occur on time scales of a few inverse lineargrowth rates – 100÷200 Alfven times – and have a ballistic character (R.B.White, PF 83) that basically differentiates them from the diffusive and localnature of weak transport.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 2
Background
2 A burning plasma is a self-organized system, where collective effects associ-ated with fast ions (MeV energies) and charged fusion products may altertheir confinement properties and even prevent the achievement of ignition.
2 Simulation results indicate that, above threshold for the onset of resonantEnergetic Particle Modes (EPM) (L. Chen, PoP 94), strong fast ion trans-port occurs in avalanches (IAEA 02).
2 Such strong transport events occur on time scales of a few inverse lineargrowth rates – 100÷200 Alfven times – and have a ballistic character (R.B.White, PF 83) that basically differentiates them from the diffusive and localnature of weak transport.
2 Observations on JT-60U (and other tokamaks) have confirmed macroscopicand rapid energetic particle radial redistributions in connection with the socalled Abrupt Large amplitude Events (ALE) (K. Shinohara, NF 01).
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 4
ALE on JT-60U (K. Shinohara, et al., Nucl. Fus. 41, 603, (2001)
Courtesy of K. Shinohara and JT-60U
ALE = Abrupt Large amplitude Event
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 5
Fast ion transport: simulation and experiment2 Numerical simulations show fast ion radial redistributions, qualitatively
similar to those by ALE on JT-60U.
0
0.01
0.02
0 0.2 0.4 0.6 0.8 1
βH
r/a
Before EPM
After EPM
G. Vlad et al., EPS02, ECA 26B, P-4.088, (2002).
K. Shinohara etal PPCF 46, S31 (2004)Courtesy of M. Ishikawa and JT-60U
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 6
Issues arising
2 Can strong fast ion transport and avalanches have any relevance to burningplasmas? Do they cause global losses or just radial redistributions?
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 6
Issues arising
2 Can strong fast ion transport and avalanches have any relevance to burningplasmas? Do they cause global losses or just radial redistributions?
2 A realistic answer cannot be independent on the dynamic formation of theplasma scenario: nonlinear wave-particle dynamics, sources, sinks, long timescales (transport).
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 6
Issues arising
2 Can strong fast ion transport and avalanches have any relevance to burningplasmas? Do they cause global losses or just radial redistributions?
2 A realistic answer cannot be independent on the dynamic formation of theplasma scenario: nonlinear wave-particle dynamics, sources, sinks, long timescales (transport). Unrealistic for now.
2 Applications to plasma equilibria given a priori. High B-field, low fast-ionenergy density operations are favored. Applications to ITER indicate fairlybenign behaviors except for the reversed shear operations. Hybrid scenariois optimal ⇒ G. Vlad et al., IT/P3-31 in Thursday Poster Session.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 6
Issues arising
2 Can strong fast ion transport and avalanches have any relevance to burningplasmas? Do they cause global losses or just radial redistributions?
2 A realistic answer cannot be independent on the dynamic formation of theplasma scenario: nonlinear wave-particle dynamics, sources, sinks, long timescales (transport). Unrealistic for now.
2 Applications to plasma equilibria given a priori. High B-field, low fast-ionenergy density operations are favored. Applications to ITER indicate fairlybenign behaviors except for the reversed shear operations. Hybrid scenariois optimal ⇒ G. Vlad et al., IT/P3-31 in Thursday Poster Session.
2 Therefore, it is crucial to theoretically assess the potential impact of fusionproduct avalanches on burning plasma operation in the perspective of directcomparisons with experimental evidence.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 6
Issues arising
2 Can strong fast ion transport and avalanches have any relevance to burningplasmas? Do they cause global losses or just radial redistributions?
2 A realistic answer cannot be independent on the dynamic formation of theplasma scenario: nonlinear wave-particle dynamics, sources, sinks, long timescales (transport). Unrealistic for now.
2 Applications to plasma equilibria given a priori. High B-field, low fast-ionenergy density operations are favored. Applications to ITER indicate fairlybenign behaviors except for the reversed shear operations. Hybrid scenariois optimal ⇒ G. Vlad et al., IT/P3-31 in Thursday Poster Session.
2 Therefore, it is crucial to theoretically assess the potential impact of fusionproduct avalanches on burning plasma operation in the perspective of directcomparisons with experimental evidence.
2 Simulation, Theory and Experiment are equally important.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 7
Nonlinear Dynamics: local vs. global processes
2 Mode saturation via wave-particle trapping (H.L. Berk et al. PFB 90,PPR 97) has been successfully applied to explain pitchfork splitting of TAEspectral lines (A. Fasoli et al. PRL 98): local distortion of the fast iondistribution function because of quasi-linear wave-particle interactions.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 7
Nonlinear Dynamics: local vs. global processes
2 Mode saturation via wave-particle trapping (H.L. Berk et al. PFB 90,PPR 97) has been successfully applied to explain pitchfork splitting of TAEspectral lines (A. Fasoli et al. PRL 98): local distortion of the fast iondistribution function because of quasi-linear wave-particle interactions.
2 Compton scattering off the thermal ions (T.S. Hahm and L. Chen PRL 95):locally enhance the mode damping via nonlinear wave-particle interactions
2 Mode-mode couplings generating a nonlinear frequency shift which mayenhance the interaction with the Alfven continuous spectrum (Zonca et al.
PRL 95 and Chen et al. PPCF 98): locally enhance the mode damping vianonlinear wave-wave interactions.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 7
Nonlinear Dynamics: local vs. global processes
2 Mode saturation via wave-particle trapping (H.L. Berk et al. PFB 90,PPR 97) has been successfully applied to explain pitchfork splitting of TAEspectral lines (A. Fasoli et al. PRL 98): local distortion of the fast iondistribution function because of quasi-linear wave-particle interactions.
2 Compton scattering off the thermal ions (T.S. Hahm and L. Chen PRL 95):locally enhance the mode damping via nonlinear wave-particle interactions
2 Mode-mode couplings generating a nonlinear frequency shift which mayenhance the interaction with the Alfven continuous spectrum (Zonca et al.
PRL 95 and Chen et al. PPCF 98): locally enhance the mode damping vianonlinear wave-wave interactions.
2 EPM is a resonant mode (L. Chen PoP 94), which is localized where thedrive is strongest: global readjustments in the energetic particle drive isexpected to be important as well.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 8
Nonlinear Dynamics of a single-n coherent EPM
2 NL dynamics of a single-n coherent EPM: neglect local phenomena andconsider only global NL EPM dynamics. Consistency check a posteriori .
2 Treat hot particle distribution consisting of a background plus a perturba-tion on meso time and space scales: the background is frozen in time.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 8
Nonlinear Dynamics of a single-n coherent EPM
2 NL dynamics of a single-n coherent EPM: neglect local phenomena andconsider only global NL EPM dynamics. Consistency check a posteriori .
2 Treat hot particle distribution consisting of a background plus a perturba-tion on meso time and space scales: the background is frozen in time.
2 The modification in the energetic particle distribution function in the pres-ence of finite amplitude fluctuations is derived in the framework of nonlinearGyrokinetics
2 The non-adiabatic fast ion response – δHk – is obtained from the NL gyroki-netic equation (Frieman & Chen PF 82). For details see TH/5-1 in FridayPoster Session.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 9
Initial value radial envelope problem
2 Using both time scale separation, ω = ω0 + i∂t as well as spacial scaleseparation, θk ⇒ (−i/nq′)∂r with ∂r acting on A(r, t) only, the initial valueradial envelope problem meso time and space scales becomes:
[DR(ω, θk; s, α) + iDI(ω, θk; s, α)]A0︸ ︷︷ ︸
= δWKT A0︸ ︷︷ ︸
,
LINEAR DISPERSION LIN. ⊕ NL EN. PART. RESP.
2 eHδφ/TH = A(r, t) = A0(r, t) exp(−iω0t), with |ω−1
0 ∂t lnA0(r, t)| � 1
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 9
Initial value radial envelope problem
2 Using both time scale separation, ω = ω0 + i∂t as well as spacial scaleseparation, θk ⇒ (−i/nq′)∂r with ∂r acting on A(r, t) only, the initial valueradial envelope problem meso time and space scales becomes:
[DR(ω, θk; s, α) + iDI(ω, θk; s, α)]A0︸ ︷︷ ︸
= δWKT A0︸ ︷︷ ︸
,
LINEAR DISPERSION LIN. ⊕ NL EN. PART. RESP.
2 eHδφ/TH = δA(r, t) = A0(r, t) exp(−iω0t), with |ω−1
0 ∂t lnA0(r, t)| � 1
2 Nonlinear (n = 0, m = 0) distortion to the hot particle distribution on mesotime and space scales: for details see TH/5-1 in Friday Poster Session.
∂
∂tHz = 2k2
θρ2
H
ωcH
kθ
TH
mH
∂
∂r
[
IIm(
QF0
ω
ωd
ωd − ω
)
Γ2|A|2]
H
.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 10
2 Assume isotropic slowing-down and EPM NL dynamics dominated by pre-cession resonance.
[DR(ω, θk; s, α) + iDI(ω, θk; s, α)] ∂tA0 =3πε1/2
4√
2αH
[
1 +ω
ωdF
ln(
ωdF
ω− 1
)
+iπω
ωdF
]
∂tA0 + iπω
ωdF
A0
3πε1/2
4√
2k2
θρ2
H
TH
mH
∂2
r∂−1
t
(
αH |A0|2)
.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 10
2 Assume isotropic slowing-down and EPM NL dynamics dominated by pre-cession resonance.
[DR(ω, θk; s, α) + iDI(ω, θk; s, α)] ∂tA0 =3πε1/2
4√
2αH
[
1 +ω
ωdF
ln(
ωdF
ω− 1
)
+iπω
ωdF
]
∂tA0 + iπω
ωdF
A0
3πε1/2
4√
2k2
θρ2
H
TH
mH
∂2
r∂−1
t
(
αH |A0|2)
︸ ︷︷ ︸
.
DECREASES DRIVE@ MAX |A0|INCREASES DRIVE NEARBY
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 3
Avalanches and NL EPM dynamics (IAEA 02)
|φm,n
(r)|
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.05
0.1
0.15
0.2
0.25
x 10-3
r/a
8, 4 9, 4
10, 411, 412, 413, 414, 415, 416, 4
- 4
- 2
0
2
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
δαH
r/a
= 60.00t/τA0
|φm,n
(r)|
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.05
0.1
0.15
0.2
0.25
x 10-2
r/a
8, 4 9, 4
10, 411, 412, 413, 414, 415, 416, 4
- 4
- 2
0
2
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
δαH
r/a
= 75.00t/τA0
|φm,n
(r)|
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
.001
.002
.003
.004
.005
.006
.007
.008
.009
r/a
8, 4 9, 410, 411, 412, 413, 414, 415, 416, 4
- 4
- 2
0
2
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
δαH
r/a
= 90.00t/τA0
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 10
2 Assume isotropic slowing-down and EPM NL dynamics dominated by pre-cession resonance.
[DR(ω, θk; s, α) + iDI(ω, θk; s, α)] ∂tA0 =3πε1/2
4√
2αH
[
1 +ω
ωdF
ln(
ωdF
ω− 1
)
+iπω
ωdF
]
∂tA0 + iπω
ωdF
A0
3πε1/2
4√
2k2
θρ2
H
TH
mH
∂2
r∂−1
t
(
αH |A0|2)
︸ ︷︷ ︸
.
DECREASES DRIVE@ MAX |A0|INCREASES DRIVE NEARBY
2 Assume localized fast ion drive, αH = −R0q2β′
H = αH0 exp(−x2/L2
p) 'αH0(1 − x2/L2
p), with x = (r − r0).
2 In order to maximize the drive the EPM radial structure is nonlinearlydisplaced by
(x0/Lp) = γ−1
L kθρH (TH/MH)1/2 (|A0|/W0) ,
2 x0 is the radial position of the max EPM amplitude and W0 indicating thetypical EPM radial width in the NL regime
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 3
Avalanches and NL EPM dynamics (IAEA 02)
|φm,n
(r)|
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.05
0.1
0.15
0.2
0.25
x 10-3
r/a
8, 4 9, 4
10, 411, 412, 413, 414, 415, 416, 4
- 4
- 2
0
2
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
δαH
r/a
= 60.00t/τA0
|φm,n
(r)|
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.05
0.1
0.15
0.2
0.25
x 10-2
r/a
8, 4 9, 4
10, 411, 412, 413, 414, 415, 416, 4
- 4
- 2
0
2
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
δαH
r/a
= 75.00t/τA0
|φm,n
(r)|
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
.001
.002
.003
.004
.005
.006
.007
.008
.009
r/a
8, 4 9, 410, 411, 412, 413, 414, 415, 416, 4
- 4
- 2
0
2
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
δαH
r/a
= 90.00t/τA0
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 11
2 During convective amplification, radial position of unstable front scales lin-early with EPM amplitude.
0
0.002
0.004
0.006
0.008
0.01
0.3 0.35 0.4 0.45 0.5 0.55 0.6
A0
(r/a)
Y = M0 + M1*XM0 -0.021507M1 0.061857R 0.99903
2 Real frequency chirping accompanies convective EPM amplification in orderto keep ω ∝ ωd
∆ω = s ωdF |x0(x0/r) (ω0/ ωdF |x=0
) .
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 12
Avalanches and transport in NL EPM dynamics
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
r/a
ωτ τ/τ = 45.00
r/a0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2A0 A0
(r/a)(β /β ) H H0
τ/τ = 45.00A0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
r/a
ωτA0
τ/τ = 132.00 (r/a)(β /β ) H H0
r/a0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2A0
τ/τ = 132.00A0
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 13
Threshold conditions for Avalanches
2 Consistency check for neglecting wave particle trapping: based on the dis-placement x0 of the avalanche front when trapping becomes important
2 Threshold for weak avalanche, or avalanche onset: x0>∼ |nq′|−1.
1 � γL
kθρH(TH/mH)1/2R−1
0
>∼ (kθLp)−1/2 ,
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 13
Threshold conditions for Avalanches
2 Consistency check for neglecting wave particle trapping: based on the dis-placement x0 of the avalanche front when trapping becomes important
2 Threshold for weak avalanche, or avalanche onset: x0>∼ |nq′|−1.
1 � γL
kθρH(TH/mH)1/2R−1
0
>∼ (kθLp)−1/2 ,
2 Strong avalanche condition: x0>∼ W0, the characteristic NL EPM width.
1 � γL
kθρH(TH/mH)1/2R−1
0
>∼ W 2
0/∆2 . ∆ ≈ (Lp/kθ)
1/2
2 W 2
0/∆2 � 1, due to the short scale of the nonlinear distortion: onset for
EPM induced avalanches is close to the linear excitation threshold.
2 If neither of these conditions is satisfied, EPM will saturate either via wave-particle trapping or other local phenomena.
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 14
Possible EPMs during Alfven Cascades in JETC
ourt
esy
ofS.D
.P
inch
esan
dJE
T-E
FD
A
20th IAEA FEC
ENEA-UCI F. Zonca, L. Chen, S. Briguglio, G. Fogaccia and G. Vlad 15
Conclusions
2 Numerical simulations and theoretical analyses demonstrate ballistic fastion transport above the EPM linear excitation threshold.
2 Nonlinear mode dynamics is an avalanche process: i.e. the radial propaga-tion of an unstable front.
2 Threshold conditions for the avalanche onset are given: typical values areclose to the linear excitation threshold.
2 Good qualitative agreement of numerical simulations with local theoreticalcalculations of EPM convective amplification.
2 Time scales and qualitative phenomenology similar to experimental obser-vations: ALE on JT-60U and fast chirping in Alfven Cascade experimentson JET.
2 Applications to ITER indicate fairly benign behaviors except for the reversedshear operations. Hybrid scenario is optimal ⇒ G. Vlad et al., IT/P3-31 inThursday Poster Session.
20th IAEA FEC