The fast-ion distribution function

Transcription

1 The fast-ion distribution function Source Collisions Orbits RF Losses W. Heidbrink

2 3 MeV & 14.7 MeV protons

3 Charge Exchange Reactivity σv

4 Complex neutral beam sources are described by a few parameters

5 Predicted Beam Deposition agrees with experiment

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7 Measured deceleration consistent with theory

8 Energy diffusion important above injection energy

9 Pitch-angle scattering rate agrees with theory Heidbrink, PPCF 43 (2001) 373

10 Many predicted orbits have been measured Heidbrink & Sadler, NF (1994)

11 Complex EP orbits are most simply described using constants of motion Projection of 80 kev D + orbits in the DIII-D tokamak Constants of motion on orbital timescale: energy (W), magnetic moment (μ), toroidal angular momentum (P ζ ) Distribution function: f(w,μ,p ζ ) Roscoe White, Theory of toroidally confined plasmas

12 Fast ions have turning points in resonance layer during ICRF

13 Fast ions have turning points in resonance layer during ICRF Predicted orbit Predicted anisotropy

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15 Homework 1. Consider alphas in ITER. Make reasonable assumptions and find a simple approximate expression for f(v). 2. Convince yourself that only the direction of the plasma current (not the toroidal field) determines the direction of the orbit shifts relative to the flux surface for co/counter injection. 3. Sketch f for these three cases. (Consider both energy and pitch.) 80 kev neutral beam injection Add RF at the 4 th cyclotron harmonic of the beam ions Raise the electron density. (This increases kperp & also has another effect.)

16 Annotated Bibliography for Winter School Lecture on the Fast-ion Distribution Function W.W. Heidbrink 1) W.W. Heidbrink and G.J. Sadler, The behaviour of fast ions in tokamak experiments, Nucl. Fusion 34 (1994) 535. I discussed material through Sec Section 5.2 is seriously dated but other sections are still reasonably accurate and current. 2) Cordey, J. G. and Core, W. G. F, Energetic particle distribution in a toroidal plasma with neutral injection heating, Phys. Fluids 17 (1974) Classic early paper on the beam-ion distribution function. 3) R.J. Goldston, Charge exchange spectra near the injection energy in tokamaks equipped with tangential neutral beams, Nucl. Fusion 15 (1975) 651. Paper based on Goldston s thesis. Section 2 has many handy approximate solutions to the Fokker-Planck equation. 4) J.A. Rome et al., Particle-orbit loss regions and their effects on neutral-injection heating in axisymmetric tokamaks, Nuc. Fusion 16 (1976) 55. Early paper that discusses stagnation orbits. 5) Roscoe B. White, The theory of toroidally confined plasmas, 2nd edition, Imperial College Press (2001). The most concise theoretical description of orbit topology is in terms of energy, µ, and P φ. White s Sec. 3.3 provides a succint summary. 6) T.H. Stix, Fast-wave heating of a two-component plasma, Nucl. Fusion 15 (1975) 737. Classic paper on fast-ion tail formed by ion cyclotron acceleration at the fundamental of a minority species. 7) Gregory Wayne Hammett, Fast ion studies of ion cyclotron heating in the PLT tokamak, Princeton Ph.D. thesis (1985). The first two chapters review ICRF theory in this unusually clear dissertation. 8) W.W. Heidbrink et al., High harmonic ion cyclotron heating in DIII- D: beam ion absorption and sawtooth stabilization, Nucl. Fusion 39 (1999) Appendix A provides simple approximate formulas for the fast-ion distribution function formed during heating at cyclotron harmonics. 1