Current Spoke Research Articles

Small-tip-angle spokes pulse design using interleaved greedy and local optimization methods.

Current spokes pulse design methods can be grouped into methods based either on sparse approximation or on iterative local (gradient descent-based) optimization of the transverse-plane spatial frequency locations visited by the spokes. These two classes of methods have complementary strengths and weaknesses: sparse approximation-based methods perform an efficient search over a large swath of candidate spatial frequency locations but most are incompatible with off-resonance compensation, multifrequency designs, and target phase relaxation, while local methods can accommodate off-resonance and target phase relaxation but are sensitive to initialization and suboptimal local cost function minima. This article introduces a method that interleaves local iterations, which optimize the radiofrequency pulses, target phase patterns, and spatial frequency locations, with a greedy method to choose new locations. Simulations and experiments at 3 and 7 T show that the method consistently produces single- and multifrequency spokes pulses with lower flip angle inhomogeneity compared to current methods.

Magnetron theory

A guiding center fluid theory is applied to model steady-state, single mode, high-power magnetron operation. A hub of uniform, prescribed density, feeds the current spokes. The spoke charge follows from the continuity equation and the incompressibility of the guiding center flow. Included are the spoke self-fields (DC and AC), obtained by an expansion around the unperturbed (zero-spoke charge) flow in powers of ν/V1, ν, and V1 being the effective charge density and AC amplitude. The spoke current is obtained as a nonlinear function of the detuning from the synchronous (Buneman–Hartree, BH) voltage Vs; the spoke charge is included in the self-consistent definition of Vs. It is shown that there is a DC voltage region of width ‖V−Vs‖∼V1, where the spoke width is constant and the spoke current is simply proportional to the AC voltage. The magnetron characteristic curves are ‘‘flat’’ in that range, and are approximated by a linear expansion around Vs. The derived formulas differ from earlier results [J. F. Hull, in Cross Field Microwave Devices, edited by E. Okress (Academic, New York, 1961), pp. 496–527] in (a) there is no current cutoff at synchronism; the tube operates well below as well above the BH voltage; (b) the characteristics are single valued within the synchronous voltage range; (c) the hub top is not treated as virtual cathode; and (d) the hub density is not equal to the Brillouin density; comparisons with tube measurements show the best agreement for hub density near half the Brillouin density. It is also shown that at low space charge and low power the gain curve is symmetric relative to the voltage (frequency) detuning. While symmetry is broken at high-power/high space charge magnetron operation, the BH voltage remains between the current cutoff voltages.

Nonlinear self-consistent theory for crossed-field devices.

A closed, nonlinear set of fluid equations that is based on the electron guiding-center orbits and is generally applicable to the analysis of crossed-field, slow-wave devices, is developed. The equations are used to model the behavior of the crossed-field amplifier. The dielectric response from the spoke charge is self-consistently included. A mean-field approximation is introduced to express the effect of the spoke charge on the rf mode profile. The dielectric modifications are then parametrized by an average amplitude factor \ensuremath{\Lambda}^ and an average phase shift \ensuremath{\psi}^ from the vacuum values. In the synchronous with the rf signal frame of reference the streamlines follow the equipotential surfaces of the transformed fields. In the steady state, the flow is incompressible. A uniform-density, constant-height electron hub feeds the current spokes. The secondary electron production at the cathode is computed self-consistently through the secondary-emission coefficient and the average impact energy. The spoke current is determined by the difference of the E\ifmmode\times\else\texttimes\fi{}B drift at the top of the hub from the rf phase velocity. At small space-charge density relative to the Brillouin density, the dielectric corrections enter as a rotation ${\mathit{e}}^{\mathit{i}\mathrm{\ensuremath{\psi}}\mathrm{^}}$ of the complex growth rate relative to the growth without spoke self-fields. The numerical solutions for arbitrary space charge are compared with previous results without spoke-field effects. An increase in the rf gain and in the anode dc current is observed at any given operation point, despite a small drop in the efficiency. It is concluded that the increase in the rf field strength in the anode-cathode space, caused by the spoke self-field, compensates for the detuning effects from the modifications on the rf mode profile. In reentrant devices, the recycling of the space charge further increases the output power and the level of noise generated by the output-input feedback.

Observation of high-frequency emissions from a critical velocity rotating plasma

The high-frequency (hf) emissions associated with the turbulent heating process, which is part of the critical velocity effect, is measured by means of hf-probes in correlation with density and floating potential. Hf-emissions are found in the front of so-called “current spokes”, as predicted by a model of the critical velocity effect in inhomogeneous plasmas. The wave spectrum and an estimate of the wave amplitudes is presented.

Determination of the Plasmaparameters and the Suprathermal Microfields in a Critical Velocity Rotating Plasma

In a critical velocity rotating plasma the profiles of the Hel 4471 Å and Hel 4922 Å lines have been investigated with high time resolution using an optical multichannel system in order to determine suprathermal electric microfields. The plasma density has been measured simultaneously with a CO2 laserinterferometer. The existence of low- and highfrequency fields is proved by the occurrence of a strongly enhanced forbidden line component and plasma satellites in the front of the current spokes, which are typical for this plasma. Thus the occurrence of electrostatic instabilities and a turbulent heating process at the critical velocity is confirmed experimentally

Occurrence and behavior of current spokes in MPD arcs

Pulsed MPD arc experiment, determining voltage characteristics and rotating current spokes occurrence and behavior

An actuator-disk model for azimuthally nonuniform MPD arcs.

Recent experiments have shown that, under some conditions of operation, the current pattern in an MPD arc is azimuthally nonuniform and rotates with a constant angular velocity, which increases with current and applied magnetic field but decreases with propellant mass flow rate. A model for such a flow is proposed which is based on the physical assumption that the current flows in a single column and upon the mathematical assumption that azimuthal averages of mass, momentum, and energy fluxes are time-in variant. The model is thus analogous to the actuator disk model, which describes the flow induced by a propeller. Additional hypotheses are made concerning flow properties and arc motion which are based on a limited experimental and theoretical understanding of magnetically balanced arc columns. A dimensionless correlation of all existing experimental measurements is derived and a criterion for the existence of current spokes is suggested.

Some Experiments on the "Spoke" Phenomenon in MPD Operation

Abstract : The problem of the appearance of a current spoke in MPD operation has attracted an increasing interest. It is the question of whether the current transfer to the anode occurs in an axisymmetric way or whether the current, or part of it, concentrates in a spoke that rotates, in other works, whether a more or less significant rotating disturbance exists. It is concluded that a spoke must not necessarily exist. Transition to the spoke from axisymmetry seems to happen gradually as destabilizing effects grow. Also we doubt whether the appearance of a rotating disturbance in current transition will necessarily entail serious deviation from axisymmetry of the downstream regions. (Author)

Experiments on current rotations in an MPD engine.

Experimental results are given which show a rotating current constriction at the anode in a conventional MPD engine. The anode is segmented into four sectors by narrow axial insulat- ing gaps. Rogowski coils measure simultaneously the a.c. current to each of the segments. Most of the,anode current is found to extend over an azimuthal spread of about 90° which ro- tates at frequencies near 100 kHz. The frequency increases with increasing arc current, in- creasing magnetic field, and decreasing mass flow. With a solid anode, evidence of this phe- nomenon is found by Rogowski coils, B loops, and Faraday cups placed in the exhaust. HE nature of the electric-current distribution in plasma accelerators has important effects on the acceleration mechanisms and electrode lifetimes. In devices with con- centric coaxial electrodes, the two extremes are an axisym- metric discharge or a localized spoke (arc column). The latter definitely exists in high-pressure arc jets. Attempts to solve the electrode spot problems in those devices led to the em- pirical discovery of the high-performance MPD engine con- cept.1'2 The essential change was the reduction of the arc chamber pressure from about 1 atm to a few torr. The addi- tion of an axial bias magnetic field had the intended result of rotating the arc so that electrode wear became uniform. To what extent the reduction of pressure and the addition of the magnetic field caused the current distribution to become more uniform (axisymmetric) remained unanswered. Understand- ably, that became a secondary question as the developers wanted to examine the promising performance of MPD en- gines. Also, the plume and electrode erosion looked axisym- metric and the performance trends were in agreement with guidelines established by theories assuming axial symmetry. If MPD engines have rotating current spokes, then one ex- pects fluctuations in the electromagnetic fields and in the plasma conditions. Fluctuations of high frequency have been observed in other cross-field plasma accelerators.3'4 At