Pfc/ja-93-5 Anomalous Electron Streaming Due to Waves in Tokamak Plasmas

. . . . . . . . Introduction . . . . . . . . Hamiltonian Guiding Center Theory Numerical Integration . . . . Interpretation of Results . . . . Acknowledgements . . . . . . References . . . . . . . . . Figures . . . . . . . . . . ii . . . . . . . . . .1 . . . . . . . . . .1 . . . . . . . . . .1 . . . . . . . . . . 2 . . . . . . . . . . 3 . . . . . . . . . . 3 . . . . . . . . . . 3 . . . . . . . . . . 4 ANOMALOUS ELECTRON STREAMING DUE TO WAVES IN TOKAMAK PLASMAS S.D. Schultz, A. Bers, and A.K. Ram Plasma Fusion Center, MIT, Cambridge, MA 02139 1. Abstract The motion of circulating electrons in a tokamak interacting with electrostatic (lower hybrid) waves is given by a guiding center Hamiltonian and studied by numerical integration. On surfaces with rational safety factor q, superposition of modes with degenerate values of the parallel mode number n + (m/q) is shown to result in electron streaming perpendicular to the magnetic field. 2. Introduction Recent work by Kupfer [1,2] on the chaotic electron dynamics induced by waves demonstrated that in the presence of four waves wherein two are of identical parallel phase velocity, an electron in resonance with the waves will have a drift in the radial direction. The work we present expands upon these results, with the intent of formulating a theory explaining the existence and properties of this "streaming". The problem is complicated by the necessity of visualizing dynamics in a four-dimensional phase space including both parallel and radial motion. 3. Hamiltonian Guiding Center Theory We use a Hamiltonian description of the electron guiding center motion that was derived in detail in [2), which makes use of several previous guiding center theories [3,4,5]. The model is based on a tokamak with an MHD equilibrium in the low-beta limit, and a low inverse-aspect ratio e = r/R. The electron is circulating, with an orbit which remains near its initial flux surface. Although magnetic field shear can be included in the derivation, it is neglected for purposes of this work. The phase space for the guiding center motion is reduced to four dimensions by gyroaveraging and assuming the magnetic moment it to be a constant: this requires that our study be restricted to waves in the low-frequency, long-wavelength limit. The derivation gives two sets of canonical coordinates for the guiding center, (z 1 ,p 1 ) and (z2,P 2 ). In terms of the familiar guiding center position (.0,6, ) and parallel velocity v11, and omitting correction terms of order E, one finds Z1 Pi ~t mRovj 1 Z2 T 06 P2 eV,#(1 Here q is the safety factor. The Hamiltonian in the absence of wave perturbations is H 0 = 2 2 + pB0 . (2) R2R