Lynton Appel with contributions from

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.