We present the first direct observation of the structure of a driven global Alfven eigenmode in a tokamak plasma using C0 2 laser interferometry.PACS numbers: 52.40.Db, 52.50.Gj The properties of Alfven waves in hot, magnetically confined plasmas are quite unlike those in homogeneous media. Despite their significance for the interpretation of both laboratory and astrophysical phenomena, experimental studies of these waves have been limited principally to the determination of the cavity eigenmode frequencies or parallel phase velocities. With the development of long confinement times in fusion experiments, laser interferometry to measure density fluctuations, and a theoretical understanding of the density fluctuations associated with Alfven waves, it has now become possible to investigate their spatial structure.We report the first such investigation, 1,2 which identifies and determines the structure of global Alfven eigenmodes (GAE). These modes are particular manifestations of the effects of magnetic confinement on the Alfven waves. Because of their relatively weak damping, the GAE can be excited to high amplitudes with an external antenna and have been previously observed as resonances in the plasma loading resistance. 3 They make up the lowfrequency part of the stable discrete spectrum of magnetohydrodynamics. 4,5 They owe their existence entirely to plasma inhomogeneities, i.e., to the coupling between the shear and compressional modes brought about by gradients in the equilibrium current and density. Rediscovered as broadened resonances in calculations based on kinetic theory, 6 the GAE have been further studied, both analytically and numerically, as candidates for the heating of fusion plasmas. 7 " 11 To model the GAE in a tokamak, we assume a cylindrical plasma of length 2TTR. The characteristic frequencies of the GAE are denoted by co /m , where / and m are the axial (toroidal) and azimuthal (poloidal) mode numbers, respectively. The plasma has axial magnetic field B 0 z and current density Jo(r), which determines the poloidal field B 0 (r), and hence the safety factor q(r) = rBjRB 9 . The wave number parallel to the field is k\\{r) = (-/+ m/q)/R, and the shear Alfven frequency is defined by co A 0) = k\\v K , where v A 0) = 2V {ponm Q ft) xl1 , n = n(r) is the plasma density, and w eff is an effective mass which depends on the impurity concentration. To include finite-ion-gyrofrequency corrections, we use the same mass, taking co ci = eBo/m eff .The characteristic frequencies of the GAE lie below the threshold of the spatial Alfven-cyclotron resonance or the Alfven continuum, defined by co 2 (l -a) 2 /(Oct) = (*)\. n That is, for these modes, / and m have opposite signs so that k\\ is nonzero and \ < 0 everywhere in the plasma. For each l,m there is an infinite sequence of eigenmodes, which may be denoted by a radial mode number. We omit this label here and consider only the lowest frequency or fundamental mode. The other modes tend to merge into the continuum as a resu...

Collisional losses from the ends of a mirror machine place substantial restrictions on the confinement time of a plasma in such a device. One method proposed to improve the viability of a mirror machine reactor is to reduce the end losses by some means other than the magnetostatic field. Such a device is called an end stopper and it has the effect of changing the loss cone of the usual mirror machine into a loss hyperboloid (two sheet). The end losses from a mirror machine with an ideal, perfectly reflecting end stopper are studied by numerically solving the Fokker–Planck equation with appropriate mirror-end stopper boundary conditions. The mirror and end stopper are assumed to be a square well system and only decay of the ions from the system is considered.

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Three-dimensional plots of dispersion in a cold anisotropic plasma are presented. The d)(k, 0) surfaces provide a clear picture of the behaviour of cold plasma waves as the direction of propagation is varied. The group velocity (do)/dk) has a simple geometrical interpretation on the surfaces.