Steady Axial Magnetic Field Research Articles

Experiments on plasma interactions with powerful R.F. discharges

Linear discharges in a steady axial magnetic field are produced in hydrogen plasmas by means of unconventional line generators. Non-decaying current pulses ranging from 1 to 50 kA at a frequency of 3 MHz. The penetration of the azimuthal oscillating field is observed, and the influence of limiters is investigated. A critical current is found, and this result is compared with the previous theory. Anomalous skin depth results from analysis of the complex wave vector, which shows energy exchanges with the plasma, in addition to the normal Joule heating. Decreasing conductivity at low densities indicates possible turbulent behaviour. An interesting feature of the discharges in the highest power range is the excitation of magnetoacoustic compressional waves at the second harmonic of the axial current with typical resonance effect. This quadratic interaction is explained with a simple model considering the pressure gradient at the plasma boundary.

Anomalous skin effect for a plasma column in a magnetic field

The influence of a steady axial magnetic field on the anomalous penetration of low frequency electromagnetic fields into a cylindrical plasma column is investigated by considering a plasma with a Gaussian electron density distribution. For this model, a complete solution is obtained for Boltzmann's equation coupled to Maxwell's equations, and the fields calculated exactly. The results show dramatic changes of the internal fields for small changes of the applied magnetic field when the average Lamour radius of the electrons is of the order of the plasma radius.

Plasma production using a standing helicon wave

A standing helicon wave has been excited by applying a transverse rf field to a cylindrical plasma immersed in a steady axial magnetic field. The predictions of the hydrodynamic theory are found to be inadequate in describing the damping.

Radio-frequency heating of a plasma

If a uniform plasma is surrounded by a heating coil in the presence of a steady axial magnetic field, it is shown that a considerable increase in power absorption may be expected if the operating frequency is chosen to be close to a magneto-acoustic resonance of the plasma column. This effect is due to a very large increase in the oscillating field at the center of the plasma column. For an initially cool plasma, heating is due to a combination of ohmic and collisional heating, while at higher temperatures, collisional heating by magnetic pumping is the dominant heating mechanism.

Experimental measurements of the characteristics of normal ionizing shock waves

A cylindrical shock tube has been used to study normal ionizing shock waves propagating, parallel to a steady axial magnetic field, into hydrogen gas at a neutral pressure of 100 mtorr. The shock velocity and post-shock parameters such as magnetic and electric fields, particle density and electron temperature are compared with theoretical calculations of these quantities obtained from the conservation equations and a modified form of the Chapman-Jouguet hypothesis. For the purposes of this calculation it was assumed that the Saha equation was applicable to the plasma. Over a range of steady axial magnetic fields from 0.65 kG to 12.5 kG and discharge currents from 20 to 160 kA, good agreement has been obtained between theory and experiment for shock velocities and for electric fields both behind and ahead of the shock. Density measurements display the predicted theoretical trend, but the measured compression ratios across the shock are low, implying a loss of particles during the ionizing process.

Charged-Particle Motion in Large-Amplitude Electromagnetic Fields

The relativistic motion of a charged particle in large amplitude, inhomogeneous electromagnetic fields is studied for several situations. This study involved the numerical integration of the equations of motion including the relativistic mass correction and the nonlinear rf v×B force term. The cases studied include particle motion in linearly and circularly polarized, homogeneous plane waves with a homogeneous steady magnetic field parallel to the direction of propagation; particle motion in linearly and circularly polarized TE-11 modes in waveguides of circular cross section immersed in a uniform steady axial magnetic field; and particle motion in cavity resonators of circular cross section (TE-111 mode) immersed in a nonuniform steady axial magnetic field. This study is concerned with the maximum energy gains possible in the above situations with field amplitudes appropriate to high-power microwave experiments. To verify the features of the particle motion as predicted in the numerical study, and to investigate effects which could not be easily included in the analysis, such as space charge from the electron beams, beam-induced cavity fields, and ionization of residual gas in a cavity resonator, certain experiments were performed. These involved the injection of 1–100-mA electron beams at 100–1000 V on the axis of circular cross-section cavity resonators (10 GHz and 1.0 GHz) immersed in a steady axial magnetic field. With pulsed operation, an energy increase of 460 keV was obtained for a drive power of 46 kW at an over-all efficiency of acceleration of approximately 10%. Higher-efficiency pulsed operation and continuous operation at lower power levels were also investigated experimentally.

New high-frequency effect due to the drift velocity of a plasma: A plasma HF analog of the Roentgen-Eichenwald current

The axial drift velocity v d of a plasma column couples the transverse electric field E c of an incoming wave to a scattered axial field E Zsc . Both the position and the angular dependence, but not the magnitude, of the resonances of E Zsc (including the complication introduced by a steady axial magnetic field) are very well explained by a cold plasma model.

Two-Stream Cyclotron and Plasma Wave Interactions

Cyclotron and plasma wave interactions between drifting electron streams in a steady axial magnetic field are studied for configurations of finite transverse cross section. It is shown for the case of equal and opposite drift velocities, that there exists an instability at approximately one-half the cyclotron frequency. This instability is a consequence of the coupling between the slow space-charge wave on one stream and backward cyclotron wave on the other stream. This coupling can occur whenever the streams are of finite transverse cross section. In order to verify some of the features of this instability, experiments in which two coaxial oppositely directed electron beams were passed between two planes, were carried out for a limited range of electron drift velocity and magnetic field values. These experiments demonstrated the existence of an instability at one-half the cyclotron frequency, in agreement with the theory. It was found experimentally that at a particular stream velocity the instability could exist over a small range of magnetic field values. The upper limit of magnetic field can be explained by the assumption that nonlinearities result in a thermalization which causes the velocity spread on the electron beam to become comparable to its mean velocity. The lower limit is a consequence of the finite length of the interaction region. Although the measured signal level was much less than that expected on the basis of converting a reasonable fraction of the beam energy to rf energy, it was found that the signals observed had a narrow frequency spread (−3 dB width was 10 kc/sec at 50 Mc/sec).

Space Charge Waves in Cylindrical Plasma Columns

When a plasma is of finite transverse cross section, space-charge waves may propagate even in the absence of a drift motion or thermal velocities of the plasma. Some of the properties of these space charge waves have been investigated by regarding the plasma as a dielectric and solving the resulting field equations. The effect of a steady axial magnetic field is considered, but motion of heavy ions and electron temperature effects are neglected. Waves are found to exist at frequencies low compared with the plasma frequency as well as waves with oppositely directed phase and group velocities (backward waves). Many of the features of these waves have been verified experimentally by measuring phase velocity and attenuation of waves along the positive column of a low pressure mercury arc in an axial magnetic field. Measurements of electron density have been made using these waves and the results are compared with those obtained by other methods. An interesting feature of these measurements, of value in plasma diagnostics, is that they can be made with frequencies which are small compared with the plasma frequency.

Interaction of a Spiral Electron Beam and a Resonant Microwave Cavity

The interaction between the electromagnetic field in a cavity and an electron beam projected along the axis of the cavity is examined. The particular cavity considered here is of the cylindrical TE11nz type in a steady axial magnetic field. If the cavity is excited in a linearly polarized mode, the electromagnetic field will drive the electrons in a helical trajectory with an expanding radius, and the electrons will excite and transfer energy to a degenerate mode oriented spatially at right angles to the driving field. In the driving plane of polarization (both planes of polarization if the cavity is excited in a circularly polarized mode), the electron beam will excite a field in phase opposition to the driving field in a manner analogous to the counter e.m.f. in an electromechanical generator. The converse case of a TE11nz cavity excited by a spiral beam of electrons is also considered.