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DECLNMER UPGRADES TO THE LLNL FLASH X-RAY INDUCTION LINEAR ACCELERATOR (FXR)The FXR is an induction linear acceleratorused for flash radiography at the Lawrence Livtmnore National Laboratory's Site 300 Test Facility. The FXR was originally completedin 1982and has been in continuoususe as a radiographictool. At that time the FXR produceda 17MeV, 2.2 kA burst of electronsfor a duration of 65 ns.An upgrade of the FXR was recentl completed. The purpose of this upgrade was to improve the performanceof the FXl by increasing the energy of the electron injector from 1.2 MeV to 2.5 MeV and the beam current from 2.2 kA to 3 kA, improving the magnetictransport system by redesigningthe solenoidaltransport fms coils, reducing the rf coupling of the electron beam to the accelerator cells, and by adding additional beam d@OStiC&We will desmibethe injectur upgradesand pdbrmanc~as well as our effbrts to tune the acceleratorby~g beam corkscrew motion and the impact of Beam Breakup Instabilityon beam centroidmotionthroughoutthe beam line as the currentis increasedto 3 kA.

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A one-dimensional crystal model is constructed with a complex periodic potential. A wave function solution for the crystal model is derived without relying on Bloch functions. The new wave function solution of this model is shown to correspond to the solution for the probability amplitude of a two-level system. The energy discriminant is evaluated using an analytic formula derived from the probability amplitude solution, and based on an expansion parameter related to the energy and potential amplitude. From the wave function energy discriminant the crystal band structure is derived and related to standard energy bands and gaps. It is also shown that several of the properties of the two-level system apply to the one-dimensional crystal model. The two-level system solution which evolves in time is shown to manifest as a spatial configuration of the one-dimensional crystal model. The sensitivity of the wave function probability density is interpreted in the context of the new solution. The spatial configuration of the wave function, and the appearance of a long wavelength in the wave function probability density is explained in terms of the properties of Bessel functions.

On p. 2472, the first sentence of the third paragraph reads that the pulse length of the conventional high-power klystrons that power the Stanford Linear Collider is 35 //sec. This should read that the correct pulse length is 3.5 jusec.