摘要:

Experimental studies of the scattering of electromagnetic waves (34 GHz) from longitudinal plasma waves (250‐500 MHz) are described. The plasma waves propagate in a 230‐cm‐long collisionless plasma column, having an electron density on axis ofne0 = 2.7 × 109cm−3and an electron temperatureTe≈ 13 eV. Scattering was observed both from plasma waves launched by a probe antenna and from waves grown up to a nonlinear saturation out of the white noise background by resonant interaction with an electron beam. The properties of these waves are accurately determined by auxiliary measurement. By using movable antennas we are able to measure the spatial growth and damping coefficients of plasma waves and to measure their absolute amplitudes. The microwave scattering is observed at a frequency displaced from the microwave frequency by the plasma wave frequency, and at an angle related to the Bragg angle. The measured frequency spectrum, angular dependence, and scattering amplitudes are compared with the theory and with rf probe measurements, giving excellent agreement in all cases.

ISSN:0031-9171    

DOI:10.1063/1.1691872

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The dispersion relation of the Kelvin‐Helmholtz instability due to a shear in ion fluid velocity parallel to the magnetic field is calculated from the Vlasov equation to account for effects of ion Landau damping and finite Larmor radius. Due to the relatively short wavelength parallel to the magnetic field, resonant particle effects are strong and the dispersion relation is considerably modified from that obtained by D'Angelo with a fluid treatment.

ISSN:0031-9171    

DOI:10.1063/1.1691873

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The nonlinear development of the two‐stream instability is investigated analytically and numerically using as a model two cold interpenetrating electron and ion streams. When periodic boundary conditions are chosen so that only one linearly unstable wave is excited, it is found that whether or not the instability levels off nonlinearly before overtaking is directly dependent upon the choice of the spatially averaged electric field E0. Simple choices of E0are given for stabilization and no stabilization. Also, even though there is strong nonlinear coupling, there is no continuous flow of energy into higher harmonics, for those waves which stabilize.

ISSN:0031-9171    

DOI:10.1063/1.1691874

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

It is proposed that the dominant nonlinear effect of low‐frequency instabilities is an incoherent scattering of particle orbits by waves. The scattering is considered to be incoherent even when only a single mode is present. Because it is incoherent, one can include wave scattering in the theory just as collisional scattering is included in the linear wave theory. A nonlinear dispersion relation is obtained from the linear dispersion relation simply by adding wave scattering terms to the collisional scattering terms. The wave scattering causes particle diffusion over the transverse wavelength and in the theory appears as an enhanced viscosity. This wave induced viscosity can be computed from the amplitude of the wave. Waves which are linearly unstable grow until the enhanced scattering causes their nonlinear growth rates to vanish. Theoretically computed values of density fluctuations, phase shifts, and flux are in good agreement with experimental values in the cases considered.

ISSN:0031-9171    

DOI:10.1063/1.1691875

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The distribution function is systematically expanded in the finite Larmor radius ordering scheme for a collisionless plasma in an axial magnetic fieldBz(x, y, t), where the magnetic field variation is a direct result of finite plasma pressure(&bgr; ∼ 1). Fluid equations are evaluated in both the guiding‐center frame and the center‐of‐mass frame. These equations are complicated by the velocity dependent ∇Bdrift which prevents strict closure of the moment equations. The effect of finite &bgr; is to include further terms in the stress tensor and in the energy equation in the form of a heat flux. An alternative derivation by a direct moment expansion is included. From these fluid equations the mechanism for producing radial differential rotation is rigorously shown. Secondly the stability of a rotating theta pinch is studied showing two finite &bgr; effects which can contribute to stability. The first is due to the increase in diamagnetic angular velocity (a result of creating a magnetic well) and the second due to the azimuthal equilibrium heat flow if the ion temperature decreases with radius.

ISSN:0031-9171    

DOI:10.1063/1.1691877

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The particle‐wave interaction to arbitrary order in perturbation theory is investigated. One finds that to every order the ensemble average distribution function obeys a diffusion equation. The diffusion constant specifies how the energy and momentum of particles change in time. By conservation of energy and momentum between waves and particles, the growth or damping rates of waves to any order can be determined. The growth rates for nonlinear instabilities and the damping rates for nonlinear Landau damping are explicitly calculated.

ISSN:0031-9171    

DOI:10.1063/1.1691878

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Electromagnetic instabilities associated with transverse plasma waves propagating perpendicular to an external uniform magnetic inductionB0are investigated for a two‐temperature Maxwellian distribution function. The analysis shows that no instability develops ifV‖e2< V⊥e2whereV‖e2andV⊥e2are the electron temperatures parallel and perpendicular toB0. ForV‖e2> V⊥e2an instability develops if&ohgr;ce2/&ohgr;pe2< V‖e2/c2[1 − (32)12(V⊥e/V‖e)]where&ohgr;ceand&ohgr;peare the cyclotron and plasma frequency, respectively, andcis the velocity of light. The allowable frequency regions for this type of electromagnetic wave to exist acrossB0are studied. It is found that below the plasma frequency there is always a narrow allowable frequency band just below any harmonics of the ion or electron cyclotron frequencies. Each width of the allowable frequency band is calculated.

ISSN:0031-9171    

DOI:10.1063/1.1691879

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

A collisionless plasma in a magnetic mirror is heated by a random electric field, acting transverse to the magnetic field. Heating occurs when the noise spectrum spans the band of electron cyclotron frequencies existing in the mirror. The electron heating rate,1.0 × 105⟨E2(V/cm)2⟩ eV/sec, is in reasonable agreement with the value predicted by a simplified theoretical analysis.

ISSN:0031-9171    

DOI:10.1063/1.1691880

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The equations of motion of electrons subject to different combinations of electrostatic waves were integrated numerically. Magnetic fields were ignored throughout. For particular choices of wave amplitude, wavenumber, frequency, and phase, and for given initial velocities, there is calculated the mean‐square velocity spreading of a collection of particles subject to three different kinds of wave spectra: (a) a single monochromatic wave; (b) several (up to 10) monochromatic waves with differing phase velocities; and (c) a single wave with a random phase change at regular intervals. Heating occurs due to two basic effects: the “trapping” of particles, operative in all three spectra, and the spreading of the spectral density due to the random phase interruptions in (c). For the parameters chosen, numerical results are that the most efficient heating occurs in case (c).

ISSN:0031-9171    

DOI:10.1063/1.1691881

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The diffusion of fast electrons in a stochastic magnetic field is considered for the simple case of the fluctuating field parallel to the steady field. The assumption defining the fast electrons is that their particle velocity is greater than the phase velocity characteristic of the fluctuating field. In the limit of observation times greater than both the Larmor period and the correlation time of the stochastic field, the diffusion coefficient can be obtained explicitly as a function of the ratio of the correlation time to the Larmor period and the result holds for all values of the ratio of these characteristic times. The result and hence the assumptions in the derivation are checked by Monte Carlo calculations.

ISSN:0031-9171    

DOI:10.1063/1.1691882

出版商:AIP    

年代:1968

数据来源: AIP