Advances in stellarator gyrokinetics


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1 Advances in stellarator gyrokinetics Per Helander and T. Bird, F. Jenko, R. Kleiber, G.G. Plunk, J.H.E. Proll, J. Riemann, P. Xanthopoulos 1
2 Background Wendelstein 7X will start experiments in 2015 optimised for low neoclassical transport Turbulence? Electrostatic instabilities: iontemperaturegradient (ITG) driven modes trappedelectron modes 2
3 W7X from above Bad curvature q (r) < 0 everywhere 3
4 Gyrokinetic stellarator codes EUTERPE global, particleincell, linear in 3D see poster TH/P449 by A.Mishchenko GENE radially local (fluxtube or fullsurface), continuum, nonlinear Both codes: electromagnetic, collisions etc. here: collisionless, electrostatic instabilities 4
5 Benchmark Linear ITG growth rate with Boltzmann electrons vs ion temperature gradient in W7X: 5
6 W7X vs LHD Global, linear ITG simulations in W7X (EUTERPE) W7X 6
7 W7X vs LHD Global, linear ITG simulations in LHD (EUTERPE) LHD 7
8 Nonlinear simulations ITG turbulence with Boltzmann electrons (GENE): rms potential fluctuations DIIID W7X 8
9 ITGs with Boltzmann electrons Nonlinear simulations with Boltzmann electrons (grad T e =0, r*=1/150): heat flux 9
10 Turbulent transport (ITG ae) So far, in W7X comparable to that in a typical tokamak, but softer : depends on r* 10
11 Trappedelectron modes Bad curvature trapped particles 11
12 Trappedelectron modes Instability requires where In an orbitconfining (omnigenous) stellarator 12
13 MaximumJ configurations But the precession frequency can be written so Stability is thus promoted by the maximumj condition Rosenbluth, Phys. Fluids
14 Physical picture The quantity, is an adiabatic invariant. E = energy. Hence, if a lowfrequency instability moves a particle radially, then implying that it costs energy to move a particle radially outward 14
15 Trappedparticle modes Theorem: collisionless trappedelectron and trappedion modes are stable if for all species a. Favourable bounceaveraged curvature. In a maximumj device, the precession drift is reversed compared with a tokamak no resonance with drift waves. 15
16 ITGs and TEMs with kinetic electrons Simulations with and without kinetic electrons (grad T e =grad T i ): growth rate for the most unstable wave number Boltzmann electrons Kinetic electrons Kinetic electrons are stabilising. 16
17 ITGs with kinetic electrons Simulations with and without kinetic electrons (grad T e =0): kinetic electrons in a flux tube 17
18 W7X, HSX and DIIID Another case: HSX simulations by Benjamin Faber, Madison 18
19 Conclusions ITG and TEM modes exist in stellarators, but display qualitative differences. turbulent fluctuations much less evenly distributed. Wendelstein 7X is, to some approximation, a maximumj device. most orbits have favourable bounceaveraged curvature Strongly stabilising for trappedparticle instabilities. ITG modes also benefit from stabilising action of the (kinetic) electrons. Less turbulent transport than in tokamaks? too early to say 19
20 Extra Material 20
21 Gyrokinetic calculation of TEMs Linear, fluxtube, electrostatic GENE simulations in DIIID and W7X no ion temperature gradient Proll, Xanthopoulos and Helander, submitted to PoP 21
22 ITGs with kinetic electrons Simulations with and without kinetic electrons (grad T e =0): growth rate for the most unstable wave number Boltzmann electrons Kinetic electrons Kinetic electrons are stabilising. Proll, Xanthopoulos and Helander, submitted to PoP 22
23 Another argument for stable TEMs In a maximumj device, the precession drift is reversed compared with a tokamak, since no resonance between precessing electrons and drift waves 23
24 Energy balance Linear, collisionless, electrostatic gyrokinetics. energy balance: Substitute the solution of the gyrokinetic equation for fastmoving partices at marginal stability 24
25 Outline of calculation Conventinal driftwave ordering Expanding in the inverse aspect ratio few trapped particles, gives electron driftwave frequency In next order, instability from waveparticle resonance only if impossible unless Helander et al, PPCF
26 Energy balance Linear, collisionless, electrostatic gyrokinetics in ballooning space: Multiply by J 0 f* and integrate over phase space. Energy balance: 26
27 Energy balance, cont d For fastmoving particles the energy transfer at marginal stability becomes Stabilising action if bounceaveraged curvature is favourable: 27
28 Algebra Conventinal driftwave ordering Expanding in the inverse aspect ratio few trapped particles, gives electron driftwave frequency In next order, instability from resonant denominator only if impossible unless Helander et al, PPCF
29 Trappedelectron modes TEMs result from overlap between bad curvature and trapping regions 29
30 Trappedelectron modes 30
31 Trappedelectron modes 31
32 Trappedelectron modes 32
33 Trappedelectron modes 33
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Q Josefine H. E. Proll, Benjamin J. Faber, Per Helander, Samuel A. Lazerson, Harry Mynick, and Pavlos Xanthopoulos Many thanks to: T. M. Bird, J. W. Connor, T. Go rler, W. Guttenfelder, G.W. Hammett, F.
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