Ohmic Field Research Articles

Electric conduction of glasses at intermediate field strengths

This study concerns four commercial glasses containing from 4 to 13 mol% alkali, a mixed alkali glass and three semi-conducting glasses containing from 5 to 10 mol% Fe 2 O 3 . Deviations from Ohm's law are detected somewhat beyond 10 4 V cm −1 and reach 10% at 10 5 V cm −1 . They are well described by a sinh function with activation lengths from 17 to 22 Å. These lengths are several Å greater than, and therefore consistent with, the saddle-point distances previously determined at the onset of Poole-Frenkel (P-F) conduction at 2 × 10 5 V cm −1 . The mechanism with a constant activation length through the ohmic and intermediate field range is thus succeeded by the P-F mechanism with the activation length decreasing as E − 1 2 . The simple electrostatic interactions required by the P-F effect imply a low density of free charges. It is suggested that the initial activation length is the radius of isolated Coulomb traps cut off at about the 1.5 kT energy level and that the effect of the field is to enhance the thermal dissociation rather than the mobility. This hypothesis invalidates the use of a sinh function to evaluate activation lengths. It is shown however that a cosh function (to describe field-assisted dissociation) can also represent the intermediate field data.

Phenomenological parameters of the spreading velocity in thyristors

In this paper the propagating wave nature of plasma spreading in thyristors was resolved by measuring the current density distribution at consecutive instants during spreading. An analytical model for the plasma spreading velocity was developed. According to this model the spreading velocity is determined by the ratio of the characteristic lengthL* of the exponential decay of the current density in the transition region to the time constant of current riseτ* of the current density at certain location. It is found thatτ* decreases with the current densityJ in the turn-on area because of the accelerating ohmic field in then-base whileL* is almost independent of the current densityJ in the operating current range. Theoretical expressions were derived forL* andτ* and compared with those measured. Satisfactory agreement was found between them.

Photoconductivity of poly((E,E)‐[6.2]paracyclophane‐1,5‐diene) and its complex with TCNE

AbstractSteady‐state photoconductivity measurements carried out for poly((E,E)‐[6.2]‐paracyclophane‐1,5‐diene) pure and sensitized with tetracyanoethylene show that doping causes a significant increase of the photoconductivity. This is due to an increase of both the hole mobility and the photogeneration efficiency. The shape of the spectral characteristic is explained by the possible existence of two paths for charge‐carrier photogeneration connected with absorption of the light by the cyclophane unit for shorter wavelengths or by CT complex for longer wavelengths. For an electric field lower than 106 V/m, the photocurrent exhibits an ohmic field dependence, and for higher fields, it becomes proportional to F1.5.

Enhanced pinch effect due to the electrostatic potential

An inward particle pinch appears necessary to explain experimental results in tokamaks. Neither the neoclassical pinch effect, which is too small, nor the off-diagonal quasilinear term, which is usually outward in the trapped particle regime, can account for the observations. A mechanism for an enhanced inward pinch is proposed, based on results for an asymmetric magnetic field bump [Phys. Fluids 15, 2211 (1972)]. Because turbulent fluctuations also break toroidal symmetry, an enhanced inward pinch driven by the fluctuations and the Ohmic inductive field E is expected. To demonstrate this effect, an inward particle flux is calculated for a model tokamak configuration that has an electrostatic potential bump Φ0 at toroidal angle ζ=2π. For the parameter regime r/R<eΦ0/Te<1, the flux is found to be Γ=−4.47K(q)(r/R)L(Φ0)(vte/Rνe) 1/2cNE/B, where r(R) is minor (major) radius, B is the magnetic field strength, vte is the electron thermal speed, νe is the electron–ion collision frequency, q is the safety factor, and K(q) and L(Φ0) are functions of q and Φ0, respectively. The results are also applicable to an asymmetric potential bump created externally to enhance the inward pinch flux of high energy, collisionless particles.

Photocurrent modeling at high dose rates

An analytical steady-state photocurrent model that includes ohmic field effects and treats (nonlinear) ambipolar diffusion and nonlinear recombination effects explicitly is developed. The nonlinear recombination and ambipolar diffusion are solved exactly, and the asymptotic ohmic field is treated as an approximate perturbation with fitted parameters. The model is found to be in good agreement with numerical calculations and with experimental results. Appropriate Taylor series expansions and extensive parametric studies using the model indicate that the superlinear response is largest and occurs at smaller dose rates in relatively high-resistivity materials that have a long excess carrier lifetime and, if the material is n-type, a large tau /sub no// tau /sub po/ ratio. The nonlinearity is more pronounced for infinite-medium devices. For this reason, power devices are expected to exhibit more nonlinear behavior than integrated circuit devices. >

Ohmic field decay and the braking indices of pulsars

It is shown that the surface dipolar magnetic field of a pulsar can vary on time-scales which are short compared to that for the longest living Ohmically decaying mode. The braking index can then deviate significantly from the value n = 3 and vary with time. Simple numerical examples are given where n < 3 for young pulsars in qualitative agreement with the observations of the Crab pulsar and PSR 1509 – 58.

Inductive Current Drive of Pinch Plasmas

The one-dimensional equilibrium code BPROF is used to calculate the plasma inductance as a function of beta and pinch parameter {theta}, and the results are represented by an algorithm. The attainable poloidal flux is calculated for a variety of cases, using the CCOIL code, to derive simple algorithms representing the ohmic heating (OH) and equilibrium field (EF) fluxes in terms of dimensionless parameters. Assuming a temperature scaling relationship with plasma current and size, the loop voltage equation is integrated to find the flux consumed versus the pulse length. This plasmas equation is combined with the flux and inductance algorithms to estimate the attainable plasma pulse length, in terms of the peak magnetic field at the coil and the plasma and coil dimensions. The attainable pulse length depends mainly on the major radius. With R = 4 m, a/R = 0.12, and I = 10 MA, a pulse length of -- 15 s is predicted.

Runaway electron distributions and their stability with respect to the anomalous Doppler resonance

The stability of nonrelativistic runaway electron distributions with respect to the anomalous Doppler resonance is examined in a range of parameters of interest to tokamaks, i.e., for Y≡ωpe/Ωce≤2 and for Ohmic electric fields ε≡E/Ec≤0.1. Distribution functions are calculated numerically within a region up to 35ve (thermal velocities) using a finite-element 2-D Fokker–Planck code. Alternatively, an analytic approximation for the runaway distribution function is used, valid beyond the critical velocity vc≂ve(Ec/E)1/2. Stability thresholds in (ω,k∥) space are then determined. For example, for Y=1 and ε=0.1, and providing that the runaway tail extends at least to 30ve, unstable waves exist having ω≤0.6Ωce and k∥≤0.03Ωce/ve.

Comparison of methods to calculate capacitances and cutoff frequencies from DC and AC simulations on bipolar devices

The question of whether or not the convenient stored-charge (SC) method is appropriate to calculate small-signal characteristics of bipolar devices is considered. A general definition of the total SC capacitance of a semiconductor device, and an expression for the difference with the AC capacitance are presented. The SC method is found to yield correct capacitance for practical p-n junction diodes at moderate and high forward bias. The discrepancy is attributed to the diffusive delay of minorities and is seen to be enhanced by ohmic fields. Nevertheless, the SC method accurately predicts the common-emitter input capacitance of a bipolar transistor with a high current gain and a low base resistance, in spite of its forward-biased emitter-base junction. The various methods proposed in the literature to derive the cutoff frequency from AC small-signal parameters are found to disagree with the SC method as well as with each other if the current gain is lower than about five. Especially at low current gain, Gummel's cutoff frequency is found to be preferable, both for simulations and for measurements. >

Equilibrium Plasma Control for a Large Tokamak with Many Poloidal Coils to Produce the Ohmic and Equilibrium Field

Plasma equilibrium control methods, based on a multivariable control technique, are formulated in the hybrid poloidal coil system, where all of the many coils are designed for ohmic heating and controlling the plasma equilibria of a large tokamak. This formulation is divided into a program control method during the buildup phase and a feedback method for controlling the plasma current and the equilibrium during the steady-state phase. The former gives programming coil currents and voltages in order to reduce the required peak power by adjusting the magnetic field profile inside the plasma, keeping the plasma equilibrium fixed. The latter includes a proportional-integral (PI) control law in the conventional optimal control theory. Effective plasma equilibrium control by these methods was obtained in computer simulations for a fusion reactor with a major radius of 5.5 m.

Theory of Runaway-Current Sustainment by Lower-Hybrid Waves

A mechanism is proposed whereby high-phase-velocity lower-hybrid waves can interact with lower-parallel-velocity electrons through nonlinearly excited plasma waves. Significant steady-state current can be sustained by the rf after the Ohmic field is turned off in a tokamak provided the initial electron distribution is in the runaway regime with density below a critical value.

Theory of Current Drive With Lower Hybrid Waves

A mechanism is proposed whereby high phase velocity lower hybrid waves can interact with lower parallel velocity electrons through non-linearly excited plasma waves. Significant steady-state current can be sustained by the r.f. after the ohmic field is turned off in a tokamak provided the initial electron distribution has a substantial runaway tail.

Microwave start-up of tokamak plasmas near electron cyclotron and upper hybrid resonances

The scenario of toroidal plasma start-up with microwave initiation and heating near the electron cyclotron frequency is suggested and examined in this paper. Microwave irradiation from the high-field side and an anomalously large absorption of the extraordinary waves near the upper hybrid resonance are assumed. The dominant electron energy losses are assumed to be due to magnetic-field curvature and parallel drifts, ionization of neutrals, cooling by ions, and radiation by low-Z impurities. It is shown by particle and energy balance considerations that electron temperatures around 250 eV and densities of 1012-1013 cm−3 can be maintained, at least in a narrow region near the upper hybrid resonance, with modest microwave powers in the Impurity Study Experiment (ISX) (120 kW at 28 GHz) and The Next Step (TNS) (0.57 MW at 120 GHz). The loop voltages required for start-up from these initial plasmas are also estimated. It is shown that the loop voltage can be reduced by a factor of five to ten from that for unassisted start-up without an increase in the resistive loss in volt-seconds. If this reduction in loop voltage is verified in the ISX experiments, substantial savings in the cost of power supplies for the Ohmic heating (OH) and equilibrium field (EF) coils can be realized in future large tokamaks.

Influence of Hall effect on the dynamics of a non-cylindrical Z-pinch

The paper studies the Hall effect in a gas-discharge plasma and its influence on the discharge dynamics. A qualitative analysis is made of the importance of the Hall effect in a non-cylindrical Z-pinch. It is shown that long before the instant of collapse of the plasma on the discharge axis, its electron component is strongly magnetized, and the Hall electric fields predominate over the Ohmic fields. The authors present the main results of a two-dimensional calculation in which the boundary conditions are used as a means of taking the Hall effect into account. The discharge dynamics obtained in the calculation are similar to the actual dynamics found for one of the non-cylindrical Z-pinch regimes.

Hall effect of hot electrons in silicon

Measurements of the Hall constant and the Hall mobility are reported for 8 Ωcm silicon at 77 K up to field strengths of 3 kV/cm and for magnetic field strengths of 2 and 8 kG. The current was parallel either to 〈111〉 or 〈100〉 or 〈011〉 crystallographic directions. The results have been found to depend critically on the individual orientations. For current parallel to «111 a planar Hall field and a dependence of the Hall data on the sign of B have been found at both ohmic and high electric fields. A theoretical explanation has been given by assuming a Maxwellian energy distribution in each valley. Acoustic intravalley and intervalley as well as ionized impurity scattering have been taken into account by assuming relaxation time tensors. From the energy balance the electron temperatures were determined. The valley populations are found to depend strongly on the magnetic field. All qualitative features of the experimental results could be explained.

Longitudinal Anisotropy of the High-Field Conductivity ofn-Type Germanium at Room Temperature

New pulse measurements of the high-field conductivity of $n$-type germanium at room temperature have been performed. Contrary to previous measurements, the conductivity is anisotropic above the Ohmic field range. The highest current for a given field is found along the 100g crystallographic axes; the 110g current is as much as 9% lower, and the 111g current 14% lower than the 100g current. The maximum anisotropy is found at a field of 3 kV/cm. No region of constant drift velocity is found; current increases with field up to 30 kV/cm, the highest field applied.

Simplified Theory of Space-Charge-Limited Currents in an Insulator with Traps

An ohmic contact between a metal and an insulator facilitates the injection of electrons into the insulator. Subsequent flow of the electrons is space-charge limited. In real insulators the trapping of electrons in localized states in the forbidden gap profoundly influences the current flow. The interesting features of the current density-voltage ($J\ensuremath{-}V$) characteristic are confined within a "triangle" in the $logJ\ensuremath{-}logV$ plane bounded by three limiting curves: Ohm's law, Child's law for solids ($J\ensuremath{\propto}{V}^{2}$) and a traps-filled-limit curve which has a voltage threshold and an enormously steep current rise. Simple inequalities relating the true field at the anode to the ohmic field facilitate qualitative discussion of the $J\ensuremath{-}V$ characteristic. Exact solutions have been obtained for an insulator with a single, discrete trap level in a simplified theory which idealizes the ohmic contact and neglects the diffusive contribution to the current. The discrete trap level produces the same type of nonlinearity discovered by Smith and Rose and attributed by them to traps distributed in energy.