A simulation of the generation of Smith-Purcell (SP) radiation at microwave frequencies is performed using the two-dimensional particle-in-cell code MAGIC. The simulation supposes that a continuous, thin (but infinitely wide), monoenergetic electron beam passes over a diffraction grating, while a strong axial magnetic field constrains the electrons to essentially one-dimensional motion. The code computes the time-dependent electric and magnetic fields by solving the Maxwell equations using a finite element approach. We find that the passage of the beam excites an evanescent electromagnetic wave in the proximity of the grating, which in turn leads to bunching of the initially continuous electron beam. The frequency and wave number of the bunching are determined, and found to be close to those proposed by Brau and co-workers in recent work. This frequency is below the threshold for SP radiation. However, the bunching is sufficiently strong that higher harmonics are clearly visible in the beam current. These harmonic frequencies correspond to allowed SP radiation, and we see strong emission of such radiation at the appropriate angles in our simulation, again in agreement with Brau's predictions. We also find that at the ends of the grating, some of the evanescent wave is diffracted away from the surface, and radiation below the threshold occurs. In addition, we observe a second evanescent wave at the same frequency, but with a different wave number. The existence of this wave is also predicted by the theory, although its presence in our simulation is unexpected. Numerical estimates of the growth of the evanescent wave are also in reasonable agreement with the predictions, although the precise form of the dependence of the gain on beam current remains hard to establish.
The properties of the axial-vector current are investigated using the dimensional-regularization scheme. The problem of defining an appropriate generalization of y , in n dimensions is discussed, and previous work is briefly reviewled. For the VVA triangle, in QED, we find that the dimensional scheme provides for vector current conservation, with the divergence of the axial-vector current anomalous. This is shown unambiguously without specifying the anticommuting nature of y, in n dimensions. If one arranges to have two species of fermions with different masses and equal but opposite couplings to the axial-vector current, the VVA anomaly is proportional to n -4, being fully canceled only at n = 4. However, the behavior of the triangle amplitude for large external momenta is reduced by two powers, and the resulting softened triangle does not give rise to any finite (as n +4) anomalies when inserted in higher-order diagrams. Finally, the appropriate generalization of y , for even-parity fermion loops is shown to be totally anticommuting, and the validity of Ward identities for two-point functions is demonstrated.E v e r since the development of dimensional regularization by 't Hooft and Veltman' it has been recognized that y5 presents special problems. At the root of the difficulty i s the fact that in four dimensions y5 has two properties which a r e incompatible f o r general n. In four dimensions, y5 anticommutes with a l l the m a t r i c e s y,. It is a l s o the antisymmetric product of four Dirac y m at r i c e s . 't Hooft and Veltrnan chose to drop the f o r m e r property in their derivation of the t r iangle anomaly. One g r e a t advantage of dimensional regularization i s that it yields amplitudes consistent with gauge invariance. T h e f o r m a l derivation of gauge invariance f r o m the perturbation s e r i e s r e q u i r e s that shifts of loop integration variables b e allowed, Dimensional regularization provides f o r that. T h e derivation of the axialvector Ward identities require, in addition, that y 5 anticommute with a l l y". Bardeen, Gastmans, and Lautrup2 have done s o m e calculations in which they p r e f e r to retain this property.The competition between vector and axialvector Ward identities was studied s e v e r a l y e a r s b e f o r e the advent of dimensional regularization. Adler3 showed that no regularization scheme can make the two consistent in the c a s e of the VVA triangle (i.e., t h e r e i s an anomaly). L a t e r , Bouchiat, Iliopoulos, and M e~e r ,~ and G r o s s and Jackiw5 showed that in a simple Abelian theory the anomaly could destroy unitarity and renormalizability. T h e s e authors a l s o showed that by modifying the theory s o that the anomaly is canceled between two different fermions, unitarity and renormalizability a r e r e s t o r e d . Since the theories w e r e Abelian, there was no need f o r dimensional regularization.The proof that non-Abelian gauge theories a r e renormalizable and unitary r e l i e s heavily on the fact that dimensional regular...
International audienceIn order to resolve problems concerning the understanding and the control of laser-induced damage of silica optical elements, a collaboration between the CEA and different university laboratories has been undertaken. Ultra-pure silica model samples, seeded with gold nanoparticles whose diameter did not exceed 5 nm, were prepared. The aim in using these samples was to observe the mechanism of damage initiation that could be attributed to inclusions of nanometric size. This paper presents the different steps encountered during this study: preparation of the samples, the laser-induced damage tests, the Nomarski and atomic-force microscope observations of this damage and a series of experiments using a time-of-flight mass spectrometer at Argonne National Laboratory. The experimental data are then interpreted, and, in particular, compared to numerical simulations. A very encouraging result is the existence of a pre-damage phase at very low fluences that is not detectable by classical optical devices. The experimental means developed for such model samples should be transposable to the analysis of industrial glasses
A simulation of the generation of Smith-Purcell (SP) radiation at terahertz frequencies has been performed using the two-dimensional particle-in-cell code MAGIC. The simulation supposes that a thin (but infinitely wide) monoenergetic electron beam passes over a diffraction grating. We simulate two configurations, one similar to the Dartmouth SP free-electron laser, with a low-energy continuous beam (we use an axial magnetic field to constrain the electrons to essentially one-dimensional motion). The other is similar to the recent MIT experiment that uses a prebunched 15 MeV beam
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