The optimal c~ and/3 values can be calculated then as ot= v/u, fl= 1/u 2.In the vicinity of u = B -l/z, v = O, Q(u, v) = (-lnB -1) -2B(u --B-I/2) zso if ~ < 0 this point is the maximum point, but if > 0 this is a saddle point and the maximum is attained at a point corresponding to the nontrivial solution of G(t) = 0. A2. Mathematical analysisWe exclude from the analysis the singular case when there exists a scale factor ). such that Fi °bs = 2F~ °~ for all the reflections, i.e. the model is ideal.The function G(t) is even, so we can consider it for t > 0 only.It is easy to see that G(t) -0 always has the trivial solution t --0, i.e. v = O, u --B -i/2 or a = 0, t5 = B.Using asymptotic formulae for the modified Bessel functions, we can obtain, for small values of t,and, for large t, lim(1/t)G(t) = 2[(AB) !/2 -C].(33)The value of (AB) 1/2 -C is always positive owing to Cauchy inequality, so G(t) = 0 has at least one nontrivial solution if the value I2 = D -ABis positive. It is possible to show, too, that the function Q(u, v) tends to -o~ when the point (u, v) tends to infinity. So, the maximum value is attained at an inner point. AbstractThe exact analytic method of evaluating the absorption during scattering in multifaceted convex crystals is developed in a way that permits efficient computation.

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We report on the first successful operation of a field-emitter-array cathode in a conventional Lband radio-frequency electron source. The cathode consisted of an array of ∼ 10 6 diamond diamond tips on pyramids. Maximum current on the order of 15 mA were reached and the cathode did not show appreciable signs of fatigue after weeks of operation. The measured Fowler-Nordheim characteristics, transverse beam density, and current stability are discussed. Numerical simulations of the beam dynamics are also presented.PACS numbers: 41.75.Fr Over the past years, field-emission (FE) electron sources have been the subject of intense investigations due to several advantages they offer over photoemission and thermionic sources. The main advantages of FE sources stem from their ability to produce very lowemittance bunched beams, their capability to generate high-average current beams, and the absence of requirement for an auxiliary laser system. A single-tip FE cathode emits electrons from a very small transverse area and can therefore produce beams with extremely small, near quantum-degenerate, transverse emittances [1,2]. When arranged as large arrays, field-emission-array (FEA) cathodes can provide substantial average currents [3] to the detriment of emittance which then scales linearly with the FEA macroscopic radius [4,5].Pulsed field-emission occurs when a FE cathode experiences a time-dependent field, e.g., when located in a resonant radiofrequency (RF) cavity. Taking the example of a cylindrical-symmetric resonant pillbox cavity operating on the TM 010 mode with axial electric field E z (r = 0, z, t) = E 0 cos(2πf t), where f and E 0 are respectively the field frequency and peak amplitude, field-emitted bunches have a root-mean-square (rms) duration σ t ≃ ω −1 [β e E 0 /B(φ)] 1/2 where ω ≡ 2πf . The latter pulse duration is obtained by taking the current density to follow the Fowler-Nordheim's (F-N) law [6] j(t) = A(φ)β 2 e E(t) 2 exp[−B(φ)/(β e E(t))] where A(φ) and B(φ) are functions of the work function φ of the cathode material and β e is a field-enhancement factor [7,8]. Nominally, the bunch rms duration is a significant fraction of the RF field period typically resulting in beams with large energy spread. This limitation can however be circumvented by exposing the FE cathode to superimposed electromagnetic fields operating at harmonic frequencies with properly tuned relative phases and amplitudes. A practical implementation of this technique consists in a RF gun supporting two harmonic modes with axial electric fields [9].In this letter we report on the first operation of a diamond FEA (DFEA) cathode in a conventional L-band RF gun nominally operated with a Cesium Telluride (Cs 2 Te) photocathode. The DFEA is composed of ungated diamond pyramids which have proven to be rugged. Depending on the size and pitch of the pyramids, tests under DC voltages have showed field emission to begin at macroscopic fields E 0 ≃ 5 MV/m, and peak currents per tip as high as 15 µA has been obtained [10].The geometry of the DFE...

The Main Injector (MI) at Fermilab is planning to use multi-batch slip stacking scheme in order to increase the proton intensity at the NuMI target by about a factor of 1.5. [1] [2] By using multi-batch slip stacking, a total of 11 Booster batches are merged into 6, 5 double ones and one single. We have successfully demonstrated the multibatch slip stacking in MI and accelerated a record intensity of 4.6E13 particle per cycle to 120 GeV. The technical issues and beam loss mechanisms for multibatch slip stacking scheme are discussed.

Lattice dynamical calculations to the full accuracy of the models are presented for the Debye-Waller B values for 17 zinc-blende-structure materials over the temperature range 1 to 1000 K (where appropriate). The materials are GaP, GaSb, GaAs, InP, InSb, InAs, ZnO, ZnS, ZnSe, ZnTe, CdTe, HgSe, HgTe, CuC1, CuBr, CuI and SiC. The models considered were the best lattice dynamical models available that have been fitted to phonon frequencies measured by neutron scattering. These include the shell model, the valenceshell model, the deformation-dipole model, the deformation-ion model and the rigid-ion model. From one to five models were used for each material, depending on the availability of published parameters. For some materials different parametrizations of the same model were examined. Intermodel comparisons show that the substantial difference in B values predicted by different models is attributable principally to the different eigenvectors they produce. Comparisons with fairly recent experimental results highlight the paucity of reliable measured values as a function of temperature and the unreliability and frequent inadequacy of models. The 14-parameter shell model is generally found to be the best.