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The infinite series of functions present in the ponderomotive Hamiltonian are explicitly summed using Newberger’s sum rule. The result is a compact and easily evaluated expression for the ponderomotive Hamiltonian. Application of the K‐χ theorem yields the linear susceptibility of relativistic magnetized plasma in agreement with, but generalizing, the previous result of Weiss and Weitzner.

Oscillatory modes of the Pierce system have been calculated. These modes are found to have growth rates comparable to the previously investigated purely growing modes. When these modes are included, it is found that the Pierce system is unstable for most values of ωp L/V0≳π.

The two‐dimensional dispersion relation for the cold‐beam, free‐electron laser is derived by applying a Lorentz transformation to the Raman decay instability of plasma. It is found that a low‐density, relativistic, free‐electron laser is actually a broad‐band amplifier; it can amplify waves throughout a frequency range of 4g2. Of these waves, the forward, high‐frequency wave has the largest temporal growth rate. However, the off‐axis, lower‐frequency waves have larger spatial growth rates. In fact, the backward waves are absolutely unstable. These low‐frequency, absolute instabilities can be very detrimental, because they have very large nonlinear saturation levels, and, hence, they can deplete the energy of the electron beam.

The fluid theory and oscillation center theory of the ponderomotive drift give apparently different results. It is shown that this difference is caused by a ponderomotive diamagnetic effect.

Kaufman’s formula [Phys. Fluids 15, 1063 (1972)] for the first‐order distribution function obtained via the action‐angle formalism is shown to be correct. The proof requires that it be noted that the transformation from canonical coordinates to physical variables has terms of all orders. Neglect of this fact has led to an incorrect formula for the linear susceptibility in previous work.

Toroidal systems of arbitrary cross section without toroidal magnetic field are analyzed via the double adiabatic fluid equations. Such systems are shown to be unstable if there exists one closed field line on which the average of κrB2 is positive, where κ is the curvature. A similar criterion is derived for linear system and is applied to a noncircular z pinch.

A SIDE FROM THE LARGE, basic textbook, nothing seems to be so firmly fixed as a key feature of the American history survey course as is the supplementary readings book or anthology. Recently, publishers have become more financially conservative and teachers somewhat more innovative in materials used, yet new collections of primary and secondary readings continue to be issued. Financial need or greed may have as much to do with the outpouring of such books as do the solemn educational purposes that are set forth in the introductions. Indeed, the obligatory paragraph on educational aims that appears in the preface is often the last we see of any educational point to these volumes. Most of these collections simply present the edited selections with no study aids for the student or guidance for the teacher. Those of us in college teaching may glance briefly at the new versions, decide they are the same as ten others on our bookshelves, and continue with the same materials we used last year. High school teachers might wish they could use one of the new collections, but be unable to do so-because the course materials are prescribed by the state or the department head, because new materials cannot be purchased every year or because they cannot require students to purchase supplementary materials. Thus, few of us are impelled to undertake a systematic review of the supplementary materials available, closely comparing the relative merits of various kinds of anthologies, the special advantages of using primary or secondary sources, the use of a problems book or of articles from American Heritage.

Computer simulations of the free‐electron laser have been carried out using a two‐and‐one‐half dimensional fully electromagnetic relativistic particle code. It has been found that waves propagating obliquely with respect to the electron beam are always unstable with appreciable growth rates and, therefore, mode competition is an important consideration in the design of free‐electron lasers. Furthermore, electromagnetic waves with group velocities opposite to the direction of electron beam propagation can be absolutely unstable. It is shown that the absolutely unstable waves can completely disrupt the electron beam and any laser oscillaton; therefore, they are extremely detrimental to the operation of free electron lasers. However, it has been found that one can stabilize the absolute instability by taking particular precautions in the design of free‐electron lasers.

A method for optimizing stellarator vacuum magnetic fields is introduced. Application of this method shows that the stochasticity of vacuum magnetic fields can be made negligible by proper choice of the coil configuration. This optimization is shown to increase the equilibrium β limit by factors of two or more over that of the simple, ‘‘straight’’ coil winding law. This method is general and ought to be applicable to other systems in which stochasticity (1) presents a problem, yet (2) is affected by the design parameters.

Rigorously sufficient and approximately necessary conditions for the absence of the beam‐Weibel instability are derived. These conditions include previously known stability criteria and resolve the seeming contradiction that these modes can be stabilized by beam temperature when the plasma is cold, but they cannot be stabilized by beam temperature when the plasma has infinitesimally small temperature.

Charged particle motion near the null of a two‐dimensional magnetic field is studied. Specifically, the magnetic field is given by the vector potential A=zψ0[(y/a)2+(ex/a)2], in which ψ0,a, and e are constants with e parameterizing the ellipticity of the flux surfaces. Conservation of canonical z momentum pz reduces the number of nontrivial degrees of freedom to two. Scaling reduces the number of parameters in the system to two, e and σ (the sign of pz ). Analytical and numerical methods are used to study the nature of orbits. The results are expressed conveniently in terms of e and Q≡(2mE)1/2/pz. When e is unity, the additional symmetry implies integrability. When e is less than unity (the case e>1 is trivially related) three regimes are found: (1) For ‖Q‖≫1 particle orbits are regular, (2) for e3/2≲‖Q‖≲1 most particle orbits are stochastic, and (3) for ‖Q‖≪e3/2 particle orbits are regular, with the third invariant being the magnetic moment.

The general expression for the ponderomotive Hamiltonian is used to obtain the quasi‐static quasi‐neutral density change caused by the ponderomotive force of a cold magnetoplasma wave of arbitrary frequency and polarization: δn (x) =−[‖E(x) ‖2−‖B(x) ‖2] /4π (Te+Ti).

The sharp‐boundary model is used to investigate the stability of straight stellarators to free‐boundary, long‐wavelength modes. To correctly analyze the heliac configuration, previous theory is generalized to the case of arbitrary helical aspect ratio (ratio of plasma radius to periodicity length). A simple low‐β criterion involving the vacuum field and the normalized axial current is derived and used to investigate a large variety of configurations. The predictions of this low‐β theory are verified by numerical minimization of δW at arbitrary β. The heliac configuration is found to be remarkably stable, with a critical β of over 15% determined by the lack of equilibrium rather than the onset of instability. In addition, other previously studied systems are found to be stabilized by net axial plasma current.

Drift and tearing modes in a sheared cylindrical collisionless plasma column are studied. A set of differential equations in the radial coordinate is derived with small gyroradius and low‐β expansion. The finite‐β effects include curvature drifts, gradient‐B drifts, and the parallel magnetic field perturbation. Algebraic elimination reduces the resulting set of equations to a fourth‐order system. Analysis shows that bad curvature does not drive the collisionless modes unstable.

The production of magnetic islands by plasma pressure in three‐dimensional toroidal systems is analyzed. Far from the rational surfaces, a procedure based on linearization in the plasma pressure applies. This yields the solution in terms of δ‐function currents at the surface. These currents are found by a nonlinear analysis valid in the vicinity of the island. The result is a set of coupled nonlinear equations determining the island widths. Scaling is found by using the approximation of nearly circular flux surfaces. The results indicate that for typical stellarators, which have a small ratio ιl0/m0 of field line rotational transform to coil rotational transform, the island size in the low‐β limit depends dramatically on whether a magnetic well is present. In this case, if a magnetic well is present, islands are insignificant; in contrast, if a magnetic hill is present, island overlap occurs for arbitrarily low pressure.

The harmonic mean method was used to calculate activity areas. Mean home range size was 5.4 ha, with a very concentrated core area of only 7.7% of the home range. Recause most animals tested exhibited shifting activity centers, and because home range size was positively correlated with the number of days a snake was tracked, it was concluded that N. sipedon at this site did not maintain a home range in the traditional sense. A dynamic methodology for quantifying areal utilization is proposed. N. sipedon was found to be very selective in its habitat utilization. Cattails (Typhus latifolia) and flooded meadow (primarily Phalaris and Carex spp.) were generally prefet ed in excess of availability, while open water was avoided. Dead cattail clumps were the most utilized substrate. Water (surface and submerged) and grass (dead and live) were also preferred to a lesser extent. Seasonal and daily trends are discussed in terms of responses to exogenous and endogenous cycles. Diversity of substrate use peaked during morning hours and showed an overall increase as the season progressed. Mean perch height was 10.9 cm above water, without strong differences among daylight hours. Perch heights were greatest during May; in habitats along open water; and on branches, dead cattails, and dead logs. The mean insolation level was 50.9%. On a daily cycle snakes received more sunlight during the midday hours, but it appeared snakes were not responding passively to decreased shade availability. Perch height and insolation level were positively correlated, thus high substrates were also associated with greater insolation. Three measures of snake activity were analyzed: incidence of movement (s = 27.7%), total rate of movement (? = 5.2 m/h), and conditional rate of movement (x = 18.7 m/h). Snakes were generally more active during April while they dispersed from the hibernaculum. From May-July the animals were equally active at all times of the day. Snakes exhibited greater rates of travel across open and exposed habitat types. Individual snakes differed significantly in all three measures of activity and also had variation in home range size spanning four orders of magnitude. Nevertheless, more active snakes did not utilize a larger area than their less active conspecifics.

The theory of the production of plasma by the interaction of a relativistic electron beam with a diatomic gas is presented. The theory includes atomic species as well as molecular species; this is shown to be necessary when nearly fully ionized plasma are produced. In addition, the theory models magnetic field diffusion by an effective time constant, which allows extensive parameter studies to be performed. The dependence of the production process on the beam intensity and width and the gas pressure is presented. It is shown that the thin beams produced by foil‐less diodes are not capable of ionizing high pressure (≳ 3 Torr) targets.