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ENEA F. Zonca, S. Briguglio, L. Chen, G. Fogaccia, T.S. Hahm, A.V. Milovanov, G. Vlad 1

Physics of Burning Plasmas in ToroidalMagnetic Confinement Devices∗

F. Zonca, S. Briguglio, L. Chen †, G. Fogaccia, T.S. Hahm ‡, A.V. Milovanov ◦,∗, G. Vlad

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

† Department of Physics and Astronomy, Univ. of California, Irvine CA 92697-4575, U.S.A.

‡ Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, New Jersey 08543

◦ Department of Space Plasma Physics, Space Research Institute, 117997 Moscow, Russia

∗ Department of Physics and Technology, University of Tromsø, N-9037 Tromsø, Norway

June 19.th, 2006

33.rd European Physical Society Conference on Plasma PhysicsJune 19 – 23 2006, Roma, Italia

∗Acknowledgments: P. Angelino, B. Coppi, P.H. Diamond, G. Falchetto, W.W. Heidbrink, Z. Lin, R.Nazikian, M. Ottaviani, J.E. Rice, B.D. Scott, K. Shinohara, R.G.L. Vann, L. Villard

33.rd EPS-CPP, I1.001


Nonlinear Dynamics of Burning Plasmas I

2 A burning plasma is a complex self-organized system where among the crucial processesto understand there are (turbulent) transport and fast ion/fusion product inducedcollective effects.

THERMAL PLASMA

FUSION PRODUCTS

ALPHA PARTICLES

FUSION PRODUCT

PROFILES

(COLLECTIVE EFF.)

FUSION REACTIVITY

(TURBULENT) TRANSPORT

COLLECTIVE EFFECTSEXTERNAL HEATING

CURRENT DRIVE



Nonlinear Dynamics of Burning Plasmas II

2 Reactor relevant conditions require fast ion (MeV energies) and charged fusion productsgood confinement:

• Identification of burning plasma stability boundaries with respect to energeticion collective mode excitations and their nonlinear dynamic behaviors above thestability thresholds

• Obvious impact on the operation-space boundaries, since collective losses maylead to significant wall loading and damaging of plasma facing materials in ad-dition to degrading fusion performance

2 Mutual interactions between collective modes and energetic ion dynamics with driftwave turbulence and turbulent transport should not deteriorate the thermonuclearefficiency:

• MeV ion energy tails introduce a dominant electron heating and different weight-ing of the electron driven micro-turbulence w.r.t. present experiments

• They also generate long time-scale nonlinear behaviors typical of self-organizedcomplex systems



The roles of simulation and theory

2 These phenomena can be analyzed, at least in part, in present day experiments andprovide nice examples of mutual positive feedbacks between theory, simulation andexperiment.

2 In a burning plasma, however, unique features not reproducible in existing experimentsare:

• energetic ion power density profiles and characteristic wavelengths of the collec-tive modes

• local power balance dominated by electron heating (fast ions) and self-organization of radial profiles of the relevant quantities: consequence on tur-bulence spectra and turbulent transport

2 Crucial roles of predictive capabilities based on numerical simulations as well as offundamental theories for developing simplified yet relevant models, needed for insightsinto the basic processes

2 Importance of using existing and future experimental evidences for modeling verifica-tion and validation



Outline

2 Collective behaviors and fast ion transport:

• The shear Alfven fluctuation spectrum: Alfven Eigenmodes and resonant modes

• Fast ion transport: diffusion and avalanches

2 Turbulence and Turbulent transport:

• Thermal ion transport: zonal flows and turbulence spreading

• Angular momentum transport: spontaneous rotation

• Thermal electron transport: dominant electron heating

2 Mutual interactions between collective modes and energetic ion dynamics with driftwave turbulence and turbulent transport

2 Examples of broader applications of fundamental physics in fusion science


Collective behaviors and fast ion transport


The role of shear Alfven waves

2 Collective behaviors due to energetic ions in burning plasmas: shear Alfven (SA) wavesplay a crucial role:

• Resonant wave particle interaction of ≈ MeV ions with SA inst. due tovE ≈ vA (k‖vA ≈ ωE)

• Group velocity is along B-field lines (ω = k‖vA): particles stay in resonance

2 Toroidal geometry plays a crucial role: SA waves propagate along B as in a 1D latticeand sample periodic potential structures with influence on SA spectrum and linear aswell as non-linear dispersion

2 Focus on non-linear dynamics and fast ion transport: conclusions largely apply toMHD modes



Shear Alfven spectrum: continuum with gaps

}EPM

W.W. Heidbrink, Phys. Plasmas 9, 2113,(2002)

2 Frequency gaps are due to lattice symme-try breaking

2 Linear theory reasonably well understood:few technical aspects need to be refined formore realistic comparisons with EXP

2 Unified description: discrete gap modes vs.resonant (driven) continuum modes.

2 Alfven Eigenmodes (AE): weakly dampedgap modes excited by fast ions; fixed fre-quency

2 Energetic Particle Modes (EPM): fast ionsdrive overcomes continuum damping; res-onant particle characteristic frequency

2 Nonlinear dynamics and fast ion transport:reflect different nature of AE and EPM



Fast ion transports in burning plasmas

2 AE modes are predicted to have small saturation levels and yield negligible transportunless stochastization threshold in phase space is reached: H.L. Berk and B.N.Breizman, Phys. Fluids B 2, 2246, (1990) and D.J. Sigmar, C.T. Hsu, R.B. Whiteand C.Z. Cheng, Phys. Fluids B, 4, 1506, (1992).



Phase space structures: fast ion resonant interactions

with AED.J. Sigmar, et al. 1992, PFB 4, 1506 ; C.T.Hsu and D.J. Sigmar 1992, PFB 4, 1492

2 Transient losses ≈ δBr/B: resonant driftmotion across the orbit-loss boundaries inphase space

2 Diffusive losses ≈ (δBr/B)2 above a s-tochastic threshold, due to stochastic d-iffusion in phase space across orbit-loss b.

2 Uncertainty in the stoch. threshold:(δBr/B)<∼ 10−4 in the multiple mode case.Possibly reached via phase space explo-sion: “domino effect” (H.L. Berk, et al.

1996, PoP 3, 1827)

Lichtenberg & Lieberman 1983, Sp.-Ver. NY



Simulation results: strongly unstable 1D system

2 Creation of phase space structures changes the distribution function thereby permittingotherwise disallowed modes to grow ( R.G.L. Vann, et al. 2005 Intl. Sherwood Conf.)





2 Strong energetic particle redistributions are predicted to occur above the EPM exci-tation threshold in 3D Hybrid MHD-Gyrokinetic simulations: S. Briguglio, F. Zoncaand G. Vlad, Phys. Plasmas 5, 1321, (1998).



Zonca et al. IAEA, (2002)Avalanches and NL EPM dynamics

|φm,n(r)|

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

x 10-3

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

= 60.00t/τA0

X1t=60

NL distor tion of free ener gy SR C

|φm,n(r)|

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

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

X10t=75

|φm,n(r)|

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

.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

X30t=90

2 Importance of toroidal geometry on wave-packet propagation and shape



Vlad et al. IAEA-TCM, (2003)Propagation of the unstable front

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0 50 100 150 200 250 300

rmax

[d(rnH

)/dr]

t/τAlinear

phase convectivephase

diffusivephase

0.025

0.030

0.035

0.040

0.045

0.050

0.055

0.060

0 50 100 150 200 250 300

[d(rnH

)/dr]max

t/τAlinear

phase convectivephase

diffusivephase

2 Gradient steepening and relaxation: spreading ... similar to turbulence





2 Strong energetic particle redistributions are predicted to occur above the EPM exci-tation threshold in 3D Hybrid MHD-Gyrokinetic simulations: S. Briguglio, F. Zoncaand G. Vlad, Phys. Plasmas 5, 1321, (1998).

2 Nonlinear Dynamics of Burning Plasmas: energetic ion transport in burning plasmashas two components:

• slow diffusive processes due to weakly unstable AEs and a residual componentpossibly due to plasma turbulence (Vlad et al. PPCF 47 1015 (2005); Estrada-Mila et al., submitted to Nucl. Fusion 2006).

• rapid transport processes with ballistic nature due to coherent nonlinear interac-tions with EPM and/or low-frequency long-wavelength MHD: fast ion avalanches& experimental observation of Abrupt Large amplitude Events (ALE) on JT60-U(K. Shinohara etal PPCF 46, S31 (2004))



Abrupt Large amplitude Events (ALE) in JT60-U

K. Shinohara etal PPCF 46, S31 (2004)

Courtesy of M. Ishikawa, K. Shino-hara and JT60-U



Fast ion transport: 3D simulation and experimentSee G. Fogaccia et al., Poster P5.073 on Friday• Abrupt Large amplitude Events (ALE) in JT60-U:

• n = 1 mode, βH0 = 8πPH0/B2 ≈ 3%;

• linear growth rate γ ≈ 0.106τ−1

A0;

• half width of the pulse ∆tALE ≈ 64.5µs;

• experimental range ∆tALE ≈ 50 ÷ 200µs;

• energetic particle profiles compare well before and af-ter ALE burst

K. Shinohara etal PPCF 46, S31 (2004)



Fast ion transport: some broader applications

2 Convective amplification of the EPM wave-packet and ballistic particle transport inAvalanche process is described by the complex Ginzburg-Landau equation (GLE)

∂2

ξ An = iγL

D

(

∆γL

γL

+L2

NL

γL

∂2

ξ

(

γL |An|2)

)

An+∆ω

DAn

ξ = r − vgrtγL ∝ αH = −R0q

2(dβH/dr)

2 For Gaussian source function αH = αH0 exp[−(ξ−ξ0)2], the GLE reduces to its canoni-

cal form; for generalized stretched Gaussian distribution, i.e., αH = αH0 exp[−|ξ−ξ0|µ]

(1 < µ < 2), the GLE is rewritten in terms of fractional derivative operators:

∇2A = q2A − p2A∇2−µ|A|2

Fractional derivative Riesz Operator

∇2−µ|A|2 =1

Γ(1 − µ)∇∫ x

−∞

|A|2(x0)

(x − x0)2−µdx0

2 The fractional derivative GLE incorporates the key features of non-Gaussianity andlong-range dependence in thresholded nonlinear dynamical systems


Turbulence and Turbulent transportThermal ion transport


Thermal ion transport: role of E × B flows

2 Better understood, compared to other transport channels

2 Ion Temperature Gradient (ITG) Turbulence: Best Candidate for χi ≫ χi,NEO

2 Role of toroidally and poloidally symmetric E × B flows and their non-linear de-correlation effect on plasma turbulence were investigated theoretically (H. Biglari, et

al. 1990, PFB 2, 1, T.S. Hahm and K.H. Burrell 1995, PoP 2, 1648) and numerically(R. Waltz, et al. 1994, PoP 1, 2229):

• Internal Transport Barrier (ITB) when (roughly) ωE×B>∼ γL

2 With recent advances in gyrokinetic codes, simulation results begin to converge forsimple cases, not only in numbers, but also in underlying physics.

2 The effective up-shift of onset con-dition for large ion heat flux iscaused by Zonal Flows

Dimits, et al. 2000, PoP 7, 949from Cyclone project



Zonal Flows are common in plasmas

Zonal Flows on Jupiter

Drift Waves

Drift waves+

Zonal flows

Paradigm ChangeP.H. Diamond, et al. 2005

PPCF 47, R35

ZFs peculiarities

• No direct radial transport

• No linear instability

• Turbulence driven



Zonal Flows regulate turbulence: effect on transport

Z. Lin, et al. 1998, Science 281, 1835

2 Transport is a local process which is predicted to scale as ∝ I: confirmed by numericalsimulations (Z. Lin, et al. 1999, PRL 83, 3645; ... 2004, PoP 11, 1099)

2 Drift wave intensity is determined by global equilibri-um properties: turbulence spreading (X. Garbet, et al.

1994, NF 34, 963; P.H. Diamond, et al. 1995, PoP 2,3685)

2 Any size scaling of turbulent transport can be reducedto dependence of I on L.



Turbulence spreading: size scaling of transport

Z.Lin, etal. 04 PRL 88, 195004

2 Turbulence spreading: local level of turbulence fluctua-tion may not be due to local free energy source

2 Turbulent transport depends on local turbulence inten-sity but it is intrinsically non-local: inadequacy of themixing length paradigm χ ≈ γL/k2

⊥

2 Impact on machine operations and burning plasma per-formance

2 Turbulence spreading is mediated by nonlinear interactions:

• Zonal Flows: importance of toroidal geometry (L. Chen, et al. 04, PRL 92,075004; PoP’04; PoP’05)

• Three wave couplings and ZFs (T.S. Hahm, P.H. Diamond, Z. Lin, et al. 04,PPCF 46, A323; O.D. Gurcan, et al. 05, PoP 12, 032303)

2 Importance of toroidal geometry and global equilibria (R.E. Waltz and J. Candy 04,PoP 12, 072303)



Turbulence spreading: some broader applications

2 Turbulence spreading can be described by turbulence intensity evolution equations inthe form (T.S. Hahm, P.H. Diamond, Z. Lin, et al. 04, PPCF 46, A323)

∂

∂tI = ΓI +

∂

∂r

(

D∂

∂rI

)

;

{

Γ = γ(r) − αIβ

D = D0Iβ ;

{

β = 1 (weak turb.)β = 1/2 (strong turb.)

2 This equation can be derived from various types of closure theories (O.D. Gurcan, et

al. 05, PoP 12, 032303): the form is that of a generalized Fisher equation.

2 Turbulence spreading is ballistic for both weak and strong turbulence regimes: turbu-lence front speed scales like (ΓD)1/2 (M. Yagi, et al. 06, PPCF 48, A409)

2 Spreading is mediated by avalanches via gradient steepening and relaxation (L Vil-lard, et al. 04, NF 42, 172; PPCF 46, B51; M. Yagi, et al. 06, PPCF 48, A409):qualitatively similar to fast ion avalanches.



High frequency E × B flows: Geodesic Acoustic Modes

2 Toroidal geometry affects toroidally and poloidally symmetric E×B flows via geodesiccurvature (finite compressibility): Geodesic Acoustic Mode (GAM) excitation at finitefrequency (N. Winsor, et al. 1968, PF 11, 2448): ω ≃ (7/4 + Te/Ti)

1/2(2Ti/mi)1/2/R

2 GAM are excited by drift wave (DW) turbulence and compete with Zonal Flows.However, they much weaker de-correlation effect on DW turbulence, due to finitefrequency (T.S. Hahm, et al. 1999, PoP 6, 922)

2 In low q region, stationary Zonal Flowspersist (higher GAM damping). Trans-port is consequently lower for lower q val-ue from gyro-fluid simulations (N. Miyatoand Y. Kishimoto 04, PoP 11, 5557)

2 Role of geodesics curvature in inhibitingturbulence suppression by ZFs has beenpointed out for edge turbulence (B.Scott03, PLA 320, 53)

2 Linear dependence of average χi on inverseplasma current is observed in global GKPIC simulations (as in EXP!)

P. Angelino, et al. 06, PPCF 48, 557

0 0.5 10

0.2

0.4

0 0.5 10

0.1

0.2

0.3

0.4

χ i/χgB

χml

i/χ

gB

IN0

/IN

IN0

/IN

See P. Angelino, et al., Poster P1.195 on Mon.


Turbulence and Turbulent transportAngular momentum transport


The role of plasma rotation

2 Plasma rotation is not only beneficial for turbulence suppression but for its stabilizationeffect on macroscopic MHD modes, like Resistive Wall Modes (RWM), which wouldotherwise limit plasma performance

2 It is still debated whether ITER will have sufficient Neutral Beam Injection (NBI)power for controlling the plasma rotation profile (NBI are source of fast ions as well)

2 Experimental evidence of spontaneous plasma rotationwithout net momentum input: extremely relevant forburning plasma operations (L.-G. Eriksson, et al. 97,PPCF 39, 27; J.E. Rice, et al. 99, NF 39, 1175)

2 Turbulent toroidal momentum flux requires turbulencek‖ symmetry breaking and has the form (B. Coppi 94,PPCF 36, B107; K. Nagashima, et al. 94, NF 34, 449)

Γφ ≈2γ

ω2

⟨

|vEr|2⟩

[

mini

du‖

dr+ 2

k‖

ω

dpi

dr

]

2 Complex interplay: Turbulence ⇒ Πr,‖ ≈⟨

vrv‖⟩

andE × B flow ⇒ symmetry breaking & turbulence sup-pression

J.E. Rice, et al. 01, NF 41, 277



Angular momentum transport

2 Nonlinear fluid (N. Mattor and P.H. Diamond 88, PF 31, 1180) as well as quasi-linearGK theories (A.G. Peeters and C. Angioni 05, PoP 12, 072515) show that χφ ≈ χi.

2 Toroidal rotation profiles in H-mode plasmas have been successfully compared withtheory predictions from Velocity and Temperature Gradient (VTG) driven modesturbulence (B. Coppi 06, BAPS 51, 186)

2 Turbulent generation of toroidal rotation: preliminary results with the flux-drivenelectrostatic ITG turbulence code ETAI3D (G. Falchetto IAEA-TM Trieste 2005)

G. Falchetto IAEA-TM ’05Non-linear fluid simulation-s in cylindrical case withzero initial parallel velocitystrong constant shear flowlayer imposed at r/a=0.75

transport

barrier

r rr

s

//

c

v

2 Constant shear flow layer induces torque in parallel flow equation & triggers a transportbarrier: finite parallel velocity generation in the region internal to the barrier.



Accretion disks and ring structuresScience 29 July 2005: Vol. 309. no. 5735, pp. 714 - 715 DOI: 10.1126/science.1116381

2 Ring structures replace accretion disks when neutral gas is substituted by plasma(B. Coppi 2006, Astr. Journal 641, 458)


Turbulence and Turbulent transportThermal electron transport


Thermal electron transport

2 In all regimes thermal electron transport has χe ≫ χeNEO: turbulent transport!

2 Possible theoretical interpretations:

• Trapped Electron Modes (TEM) + ITG with trapped electrons: long wavelength

• Electron Temperature Gradient (ETG) driven modes: short wavelength

• Magnetic Flutter: e.m. turbulence (See B. Scott, Invited I3.003 on Wed.)

2 Dominant electron heating from fusion alphas: burning plasmas will have differentweighting of electron driven micro-turbulence

A.G. Peeters, et al. 05 NF 45,1140

2 Density profile peakedness: competition between ITG-induced inward and TEM-induced outward particlepinch: low collisionality burning plasmas have Ln ≈ a(C. Angioni, A.G. Peeters, et al. 04, NF 44, 827; ... 05NF 45, 1140)

2 Results confirmed by recent non-linear gyrokinetic sim-ulations (C. Estrada-Mila 05, PoP 12, 022305). To becontinued...



ETG turbulence and electron transport

2 Electron transport remains anomalous even when long wavelength modes (ITG/TEM)are so reduced that ion Internal Transport Barrier (ITB) are formed: reduced ion heatand particle transport (E. Mazzucato, et al. 96, PRL 77, 3145).

2 ETG saturated phase dominated by streamers (F. Jenko, et al. 2000, PoP 7, 1904;W. Dorland, et al. 2000, PRL 85, 5579) and much weaker role played by ZFs: ETGmay cause turbulent transport at level of EXP interest.

F. Jenko, et al. 2000, PoP 7, 1904

2 Global numerical simulations (GK & Fluid)find smaller transport due to ETG

2 No clear evidence of scaling of ETG inducedtransport with the radial streamer size

Z. Lin, et al. 2005, PoP 12, 056125


Mutual interactions of collective modes with drift wave turbulence


Physics issues behind fluctuations non-linear interac-

tions

2 Interaction between collective modes and thermal plasma turbulence:

• collective modes due to energetic particles

• plasma turbulence due to thermal components

2 Intrinsic separation of spatial scales (orbit size) in the free energy source: interactionoccurs

• if the time scales become comparable such as for Alfven ITG (e.m. ITG)

• if mediated by the 3rd entities such as zonal structures: zonal flows, fields,corrugations of radial profiles



Mutual interactions of collective modes with DW tur-

bulence

2 E.m. plasma turbulence: theory predicts excitation of Alfenic fluctuations in a widerange of mode numbers near the low frequency accumulation point of s.A. continuum,ω ≃ (7/4 + Te/Ti)

1/2(2Ti/mi)1/2/R (F. Zonca, L. Chen, et al. 96, PPCF 38, 2011; ...

99, PoP 6, 1917):

• by energetic ions at long wavelength: finite Beta AE (BAE)/EPM

• by thermal ions at short wavelength: Alfven ITG

2 Magnetic flutter: may be relevant for electron transport (B.D. Scott 2005,NJP 7, 92;V. Naulin , et al. 2005, PoP 12, 052515)

2 Recent observations on DIII-D confirm these predictions (R. Nazikian, et al. 06, PRL

96, 105006)


ENEA F. Zonca, S. Briguglio, L. Chen, G. Fogaccia, T.S. Hahm, A.V. Milovanov, G. Vlad 29R.N

azikian

,et

al.

06,PR

L96,105006

R. Nazikian, et al. 06, PRL 96, 105006



2 The same modes are excited by a large amplitude magnetic island on FTU (P. Buratti,et al. 2005, NF 45 1446; See S. Annibaldi, Oral O2.016 on Tues.).

n=-1, m=-2 tearing mode Locking & unlocking

n = -1 HF mode

n=+1

P. Smeulders, et al. 2002, ECA 26B, D5.016



Long time scale behaviors2 Depending on proximity to marginal stability, AE and EPM nonlinear evolutions can

be predominantly affected by

• spontaneous generation of zonal flows and fields (L. Chen, et al. 2001, NF 41,747; P.N. Guzdar, et al. 2001, PRL 87, 015001)

• radial modulations in the fast ion profiles (F. Zonca, et al. 2000, Theory of

Fusion Plasmas, 17)

EPM NL dynamics (F. Zonca, et al. 2000, Theory of Fusion Plasmas, 17)

2 AITG and strongly driven MHD modes behave similarly



Zonal Flows and Zonal Structures

2 Very disparate space-time scales of AE/EPM, MHD modes and plasma turbulence:complex self-organized behaviors of burning plasmas will be likely dominated by theirnonlinear interplay via zonal flows and fields

2 Crucial role of toroidal geometry for Alfvenic fluctuations: fundamental importanceof magnetic curvature couplings in both linear and nonlinear dynamics (B.D. Scott2005,NJP 7, 92; V. Naulin , et al. 2005, PoP 12, 052515)

2 Long time scale behaviors of zonal structures are important for the overall burningplasma performance: generators of nonlinear equilibria

2 The corresponding stability determines the dynamics underlying the dissipation ofzonal structures in collision-less plasmas and the nonlinear up-shift of thresholds forturbulent transport (L. Chen, et al. 2006)

2 Impact on burning plasma performance



Conclusions

2 Burning plasmas are complex self-organized systems, whose investigation requires aconceptual step in the analysis of magnetically confined plasmas.

2 Integrated numerical simulations are crucial to investigate these new physics; whilefundamental theories provide the conceptual framework and the necessary insights.

2 Verification against experimental observations in present day machines is a necessarystep for the validation of physical models and numerical codes for reliable extrapola-tions to burning plasmas.

2 Lack of understanding of some complex burning plasma behaviors can be likely filledin by increasingly complicated and more realistic modeling of plasma conditions ascomputing performances improve.

2 However, some other unexplained behaviors may be just indications of fundamen-tal conceptual problems: mutual positive feedbacks between theory, simulation andexperiment will be necessary.

2 Burning plasma physics is an exciting and challenging field: many examples of funda-mental problems with broader applications and implications.


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