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Investigating Compressional Alfven Modes (CAEs) on MAST: Measurements, Calculations, and Insights

This study examines Compressional Alfven Modes (CAEs) observed during the MAST experimental campaigns, revealing significant electromagnetic activity above traditional TAE and EAE frequency ranges. The research details over 10 discharges, highlighting energetic particle distributions and eigenmode calculations, essential for understanding these quasi-steady-state phenomena. It discusses the possible mechanisms for anomalous heating, high-frequency activity patterns, and the influence of collective plasma behavior. Findings contribute valuable insights into plasma diagnostics and stability, advancing fusion research.

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Investigating Compressional Alfven Modes (CAEs) on MAST: Measurements, Calculations, and Insights

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  1. CAEs on MAST Lynton Appel with contributions from Rob Akers, Tunde Fülöp1, Richard Martin and Hagen Smith1, EURATOM/UKAEA Fusion Association, Culham Science Centre, OX14 3DB. UK, 1Department of Electromagnetics, Chalmers University of Technology, and EURATOM-VR Association. This work was jointly funded by the UK Engineering and Physical Research Council and EURATOM

  2. Introduction • Background to CAEs. • Measurements of CAEs on MAST. • Calculations of energetic particle distribution. • Eigenmode calculations • Conclusions.

  3. Background to CAEs • Compressional Alfvén Modes (CAE)s are quasi steady-state electromagnetic activity occurring well above the TAE and EAE and gaps. • kvA,k||<< k , . • . • Edge-localised modes on outer-edge of plasma. • Mode drive from “bump-on-tail”, v>vA. • Significance of CAEs • possible mechanism of anomolous heating [Gates, D et al PRL 87, 2001] • useful diagnostic of outer plasma regions • Can exist at higher  than TAEs, since Landau damping is weak (k||<< k ).

  4. Example from NSTX Gorelenkov et al, Nuc Fusion 42, 2002. Multiple CAE modes identified at 0.22> ci> 0.73 TAE gap (approx)

  5. CA eigenmode • For waves with < c andk||<< k dispersion relation for low-toroidicity reduces to the 1-D Schrödinger equation [Gorelenkov 1995]: where MAST Discharge 9429, t=280msec m=13, f=2MHz potential well

  6. Measurements of CAEs on MAST • Activity observed in >10 discharges during the MAST EBW campaign. • Ip=750kA, Rmag=0.86m, a=0.53m, vA(Rmag)=9.7105m/s, fc(Rmag)=3.8Mhz, =1.9 • Steep edge density profile. • Discharges have regular sawteeth and elms; “steady-state” apart from ramping density. • NBI heating: 1.5MW,47keV (Deuterium) from t=100msec, Efast=8kJ, 2<vbeam/vA<3. • ECRH: up to 800kW in some discharges => not primary drive mechanism.

  7. High-frequency activity • Long-lived activity ~100msec • activity in two frequency bands • slow +ve frequency drift: f(0.3s)=2f(0.2s) modes numbers are sequential in n within each band • Activity ceases for a short time after each sawtooth crash • Nyquist frequency is 1MHz! • modes and beam ions rotate in opposite direction • f vA<1 • => so transform to f2hfnyq-f (h=1,2,3,…):

  8. High-frequency activity (2) • Transforming to 3MHz<f<4MHz, • Eigenmodes and beam ions rotate in same direction • . For 190ms<t<300ms, f=-8.3%, and vA=-9.5%. • vA (axis)

  9. Energetic particle distribution • NBI-heated fast particle distribution computed by LOCUST on discharge 9429 (t=280ms). • In physical coordinates and • Distribution function mapped to constants of motion space, • Orbits classification of fast-particles • 40% co-passing • 40% trapped • 12% counter-passing • 8% co-passing prompt • Distributions exhibit bump-on-tails (f/ E>0 and f/ >0 ) in all particle classes.

  10. Evidence for bump-on-tail distribution • Co-passing + trapped ions • bump-on-tail in f(E) for p>pcritdue to density accumulation at stagnation points.

  11. CA mode drive • Mode drive has been estimated using the large aspect ratio (l.a.r.) theory of Gorelenkov [Phys Plasmas 2 (1995)p1961] • The mode growth is (Summation is over all resonance locations) • Calculation of mode drive is obtained using numerical equilibrium and fast-particle distribution (MAST discharge 9429, t=280ms). • Primary drive is from bump-on-tail in f(E). • Modes become unstable if f/ E>0 is boosted by 5. • Results are only “a guide” due to approximations:l.a.r., E>>Er and < ci.

  12. Calculation of eigenmodes • Apply theory of Smith et al [Phys Plasma 10 (2003)p1437] to compute CAEs • Theory includes effects of finite toroidicity and ellipticity, with k||<<1. • Poloidal variation adopts a ballooning representation (but with j=0): Hermite Polynomial with the prescription ; Equilibrium profiles have the form ; ; ;

  13. Potential well • Potential well extends from 25cm to near plasma edge (0.5<r/a=0.95). CAEs located in well

  14. Locations of CAEs • 1230 CAEs computed ( , , ). • for n>0 often >2 CAEs for a given triplet (n, p, s), situated in two radial bands. • Measured activity corresponds to outer modes o~47cm (r/a=0.9). • Separation of eigenfrequencies, mostly consistent with large measured frequency separation. • Eigenvalue spacing cannot account for measured fine-scale frequency splitting. (measured)

  15. Poloidal/radial extent of CAEs • Edge-modes become more localised in poloidal () and radial dimensions () with increasing n. • Boundary conditions of eigenvalue code ( ) are incompatible with for outer mode . o~47cm

  16. Effect of magnetic well • Addition of magnetic well results in an additional class of higher-frequency modes. Eigenmodes in outer well

  17. Conclusions • High-frequency activity well above the TAE/EAE frequency range has been observed on MAST. Activity is long-lived and exhibits a 100% frequency drift. • Transforming to a frequency range 3-4MHz, the frequency drift becomes proportional to vA with mode rotation in the NB-ion direction. • The NB population exhibits bump-on-tails in energy and  to provide the required mode drive. • Calculations have obtained a large number of CAE modes and can explain the frequency difference between bands. However the fine-scale splitting cannot be accounted for. • Further measurements are planned with new digitizers sampling at 10MHz.

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