No abstract

No abstract

out separately, by means of an axially and radially movable probe. We found, by interferometry, that the wave signals were primarily concentrated within the axial length of the T probes or grids. When the detecting probe was outside of this region, the signal dropped by 60 dB. Our measurements indicated that in the axial direction the waves were essentially standing waves, with the dominant Fourier components having twice the probe lengths; i.e., k^ir/l', etc. Thus, by approximating the standing waves in the axial direction with cosik^z), cos(k/z), we find from theory that for k ]l «k x the dominant contributions to the matrix elements are given by k || =k "' + k [,". By varying the lengths of the receiving and transmitting probes in the nonlinear Landau damping experiments, we have verified that this model of wave excitation gave good agreement with theory, In summary, we believe that we have observed experimentally nonlinear Landau damping of plasma waves in the presence of an external magnetic field. The qualitative features of the experimental results agreed well with the predictions of the nonlinear Landau damping theory. In particular, the observed decay of a finiteamplitude wave into a single perturbed wave cannot be explained by resonant mode-mode coupling or parametric theory. The amplitude variation of the perturbed wave as a function of the pump wave followed the predictions of the third-order theory, through at least four decades. The measured nonlinear wave-particle coupling coefficient was found to agree with theory within ex-perimental error. A detailed account of this work will be published elsewhere.We are very grateful to Professor M 0 N. Rosenbluth and Professor B c Coppi for invaluable discussions. . 5 M. Porkolab and R. P. H. Chang, Phys. Rev. Lett. 22, 826 (1969). 6 R. P. H. Chang and M. Porkolab, to be published. 7In the spatial case, the finite parallel wave number cannot be neglected in nonlinear Landau damping theory in a nearly collisionless plasma. 8 The dispersion curves shown in Fig. 1(b) are those with &n =0. Nevertheless, for the experimentally measured values of k^/hjfiw «kj), it can be shown that the real parts of k L and oo are closely approximated by the curves used.Electron cyclotron waves are shown to grow unstably in the presence of small relative drifts of a warm ion distribution perpendicular to the B field. Numerical simulations show that this instability causes anomalous diffusion of plasma across the magnetic field and heating of the electron thermal spread to values much greater than the relative ion-electron drift velocity.Most methods for heating and confining high-temperature plasma involve a flow of electric currents normal to magnetic field lines in the plasma. This Letter reports the theoretical properties of a highfrequency electrostatic plasma instability which is driven by the relative drift of ions and electrons in such a normal current flow and which is expected to occur and cause anomalous resistance to the current in a wide range of applications. The calcu...

No abstract

cause our data are at large "superheating," a quantitative comparison must await either equation-of-state data in metastable states or further lifetime measurements without the complication of a fill hole. We cannot now state whether the abruptness of the decrease in lifetimes is in agreement with nucleation theory or results from another source such as the onset of large scale instability.We never saw evidence of metastability when Pmean had the values 0.68p c , 0.90p c , 0.94p c , 1.02p c , and 1.05p c . The observations at 0.68p c , 0.90p c , and 0.94p c imply that there is no barrier to nucleation of a droplet in the calorimeter, a situation which is expected if He 3 wets the walls of the calorimeter. The observations at 1.02p c and 1.05p c lead us to infer that very near T c the density at the top of the fill tube was less than p c . (The linear model predicts that metastability will not occur in our calorimeter if p mean ^ 1.064p c and wetting occurs.)To summarize, we have reported the comparative ease of obtaining metastable thermodynamic states of He 3 and measuring their properties. We find that specific heat is continuous at the onset of metastability. Near the critical point the range of metastable states changes in qualitative agreement with a calculation showing a decrease in the rate of homogeneous nucleation. A detailed test of nucleation rates should be possible with further measurements of this type.The nonlinear development of current-driven electron-cyclotron turbulence perpendicular to a background magnetic field 1 ' 2 is important for understanding the anomalous resistance observed in collisionless-shock experiments. 3 Based on the results of numerical simulations, we outline a model of the strong turbulence which is quite different from the picture of Lampe et at. 4 and is in disagreement with many of their conclusions, particularly in the parameter range of high-/3 shock experiments. We find that there are three . Our qualitative conclusions would be unchanged had we used the critical isotherm or critical isochore derived from the multiparameter fit of all the Wallace and Meyer data to the equation of state of M. Vicentini-Missoni, J. M. H. Levelt Sengers, and M. S. Green, J. Res. Nat. Bur. Stand., Sect. A 7£, 563 (1969). The latter equation of state has three coefficients and two exponents. It requires the introduce tion of a sixth parameter for extrapolation into the metastable region. 10 A. Eggington, C. S. Kiang, D. Stauffer, and G. H. Walker, Phys. Rev. Lett. .26, 820 (1971).physical regimes exhibiting different nonlinear electron behavior depending on the relative size of the wavelength X of the turbulence compared with the electron gyroradius r e . For high-0 shock experiments where X = 27r/£«r e , the electrons can be trapped in potential wells for longer than an electron gyroperiod, thus giving rise to a nonlinear electron-cyclotron instability which does not have the properties of the nonmagnetic ion-acoustic instability. This instability causes substantial electron heating and ...