The magnetic mirror approach to fusion is reviewed in depth. Starting with a brief chronological history of the development of the basic mirror concept, its subsequent evolution into the tandem mirror, the field reversed mirror and other variants is described. Also discussed are the many-faceted aspects of mirror theory, including adiabatic invariants, MHD equilibrium and stability, collisional processes, transport theory and microinstability theory. The review concludes with an updating of experimental results, a discussion of mirror-related technology, including neutral beam injection and direct conversion, and a brief description of design studies of mirror fusion power plants.

Three classes of electrostatic instabilities deemed likely to be encountered in magnetic mirror-confined plasmas are examined theoretically: (A) a convective type, maser-like in nature, with waves propagating essentially parallel to the field lines; (B) a nonconvective (absolute) instability, arising in the presence of radial density gradients; and (C) a limiting case of (B), not requiring radial density gradients for its stimulation. All three instabilities, which owe their origin to the loss-cone nature of the particle distributions, exhibit critical conditions for onset or growth that are sensitively dependent on the shape of the distribution functions. These conditions are least restrictive for plasmas that have reached a state of collisional equilibrium in confining fields of high mirror ratio. In this limit (C) disappears and the critical conditions imposed by (A) and (B) are not unduly restrictive. In particular, at high plasma densities it is required: (1) for adequate stability against (A), the length of the plasma between the mirrors must not be greater than about 300 to 500 ion-orbit radii, and (2) to satisfy conditions (on the radial density gradient) imposed by (B), the plasma dimensions transverse to the field must also be of the same order; i.e., the plasma must be roughly spherical. Examples are also given which show that the confinement of highly peaked distributions leads to required conditions of orders of magnitude more restrictive than those found for well-randomized distributions.

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S CINTILLATION counters are being used increasingly for applications that require extremely short resolving times. In this letter, we discuss the limitations on resolving time that arise from fluctuations in the emission, transmission, and collection of scintillation photons. For this purpose we assume that following excitation of the scintillator by an energetic event, the photomultiplier multiplies the primary photo-electrons without time spread, and that the resulting pulses are fed into a discriminator that gives a signal when it has accumulated a definite number, say Q, of pulses. We ask for the fluctuation in time of these signals. Except for the neglect of time spread in the photo-multiplier, this model contains the essential features of actual counting systems.The average or expected number of photo-multiplier pulses between the initial excitation of the scintillator at zero time (allowing for a possible constant time delay in the photo-multiplier) and time t is /(/), where /(0) = 0, / is a continuous monotonically increasing function 1 of t, and df/dt is piecewise continuous. It is assumed that the probability that N pulses occur between 0 and / is given by the Poisson distribution:This means that either (a) a relatively small, randomly selected, sample of the emitted photons is converted into output pulses, or (b) the magnitude of the initial excitation is randomly distributed, 2 or both. Then the probability that the Qth pulse occurs between t and t-\-dt is 3The total probability that the Qth. pulse occurs between 0 and *> iswhere Rasf() is the average total number of primary photoelectrons. It is readily verified by comparison of Eqs. (1) and (3) that IQ(R) is the probability that Q or more pulses occur between 0 and co, as it should be. IQ(R) can be evaluated from Eq. (2), or found from tables of the incomplete gamma-function. 4 The variance of the signal time is ^<* 2 >Av-£ 2 = 1 IQ(R) JO >^«M^r^HIt may also be calculated from a generating function: 5If we define the inverse function to f(t) as t = g(f), then Eq. (4) becomes G(x)~-^j; R x^f^e-fdf.As a simple example, 6 we consider the case f(t) = X/ (not applicable to scintillation counters), in which case R-«o and g(/)=//X: G(x) = (l-X~1 ln*)-«, i=(dG/dx) Xmml~Q /\ v=Q/\*=t 2 /Q. For a scintillator, R must be finite, and g(f) has a singularity at the point f=R. It is apparent, however, that the integral over / that gives (^)AV diverges if and only if the nth moment of the probability function (2) diverges, so that any difficulties caused by the singularity can easily be traced.When R is finite, G{x) and v cannot be written in simple closed forms. However, in the physically useful case R^>1, R^>Q, Eq. (3) shows that we can put IQ(R)^1, and simple asymptotic expressions can be obtained that involve only the behavior of /(/) near / = 0. Suppose that then f(t) = a 1 t-\-a 2 t 2 +>--In general, oi, a 2 , • • • are proportional to R, so that h oc 1/R i b%

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