of space charge produce3 no emittance .... or promotional purposes or for creating new collective works for resale or redistribution to servers .... rent constant.
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1794
IEEE TransactIons on Nuclear Science. Vol. NS-32. No. 5, Octobsr 1985 PARTICLE-IN-CELL Michael Applied Los Los
SIMULATIONS
E. Jones and William K. Peter Theoretical Physics Division Alamo3 National Laboratory Alamos. New Mexico 87545
Introduction The laser-won cl.21 is a device (either RF or DC) for p-oduc:ng intense, very short, pulsed electron beams (Lens of picoseconds). In the DC lasertron, a laser is pulsed repetitively onto a photoemissive cathode In general, the current is not space-charge [31. limited and follows the laser intensity. The electron pulse is then accelerated out of the device by a constant voltage. By using the laser the need for a In the RF subharmonic buncher is eliminated. This imthe diode becomes an RF cavity. lasertron, proves the breakdown characteristics of the device, allowing higher voltages to be applied and hence Tne calculations are higher currents to be obtained. aimed at prcducing a 10 nC electron beam with an emittance of less than 4On mm-nrad for use in freeelectron laser experiments at Lo3 Alamos C41. Other applications of the lasertron include efficient microwave or RF generation [?I. A class of electrode shapes [see Eq. (211 ha3 b een obtained which in the absence of space charge produce3 no emittance growth. These shapes have been studied with the particle-incell simulation model ISIS [51, and the electrodes which produce minimum emittance including the effect Unique emitof space charge have been determined. tance problems associated with the time dependence of the beam pulse are studied and condi'.ions for reducing these effects are discussed. Sources
of
OF THE LASERTRON
realizable systems, the region of interest must be bounded by three electrodes, a3 shown in Fig. 1. If electrodes at the indicated potentials are placed as shown in the figure, the vacuum electric field will be linear everywhere in the region enclosed by the conductors. In practice, thi 3 solution can only be approximated. Figure 2 shows the electrode approximation used in an actual ISIS calculation (z. is chosen to be 3 cm). The $ - 0 (cathode) and y - 0.85 (anode) electrode3 are truncated and the third electrode is completely absent. It can be expected that this electrode configuration will give a good approximation to the solution of Eq. (1) near the origin. Also the electrodes pass only through the mesh points oI the finite difference grid as shown in Fig. 2. There are two classes of diodes which can be obtained from this solution. For 0 < u < 0.5, the cathode tilts toward the anode as shown in Figs. 1 and 2 (u - 0 gives a flat catho,de). This causes the beam
Emittance
In charged electric
the paraxial approximation, emittance in particle beams arises from nonlinear radial linear in fielcs. Thus if E is everywhere r the radial coordinate r. the dynamics of the particles will be self-similar and no emittance will be The electric field in a diode is produced produced. by the electrode shapes and by the space charge of the Either field can be nonlinear beam that is created. In order to and consequently a source of emittance. minimize the emittance we begin by requiring the field produ-ed by the electrodes be linear. The solution to Laplace’s equation, assuming which produces only linear radial axial symmetry, electric fields can be written as + [ p2(r-d/2
6-5
- 3.5, the cathode bend3 away from the anode, which causes defocussing. The case IJ * m produces an axial eifCtPiC field iJhich is indebendent of r. Fsr high perveance beams, another source of emittance is nonlinear space-charge forces. Because the Current emittec by the lasertron is controlled by the laser, the current density can be made radially uniform by using a uniform laser illumination. However, space-charge forces tend to retard the partlcles near tne axis. This causes the radial charge density to become nonuniform, prod,Jcing nonlinear radiai electric fields and emittance grouth. This effect can be minimized by choosing the vacuum field3 to have the opposite effect, i.e., accelerate particles faster near the axis. From Eq. (1) it can be seen that the solutions wnich accelerate the particles on axis faster, at least near the cathode, are the fociJssing sol,Jtionz (0 < u < 0.5). Preclzely ‘which value of p minimizes the velocity shear of the space density in the beam. charge depend3 on the current The time dependence of tne current pulse in the lasertron introduces a further source of emittance reEven if the diode lated to the space charge. parameters were chosen to minimize the effect3 cf nonlinear space charge for the steady state case, the ends of the beam will not be leading and trailing This is becailse the beam expands properlY handled. under its on space charge more in the center of the Thus the expansion is not beam than at the ends. self-similar and an emittance measurement detect3 these end effects as increased emittance. Simulation
Method
and Results
Simulations for a wide variety of diode configurations and parameters have been performed with the 2-dimensional, relativistic, electromagnetic particle-in-cell simulation code ISIS. The laser controlled emission is modelled by placing an upper bcund Elozt on the current density emitted by the cathode. of the calculations use a step-function laser pulse, but other temporal profiles, including trapezoidal The emlttance numbers quoted here are a were used. r.ormalized rms emittance measured as the beam exit3 The the simulation region (to the right in Fig. 2). rms calculation is carried out over a time interval long enough to obtain a good statistical sampling of For pulsed beams this interval is chosen particles. in the pulse, long enough to sample all the particle3 typically 5 to 10 tho,JSand. The calculation3 use a system of dimensionless variables in which the space variables scale with a parameter A and the time variable’zcales with X/c, For example, the calwhere c is the speed of light. culation shown in Fig. 2 is labeled as if A is taken Thus the calculation Is for a diode with to be 1 cm. a 0.56 cm radius emitting cathode and a 50 ps laser choosing A to be 10 cm for example, pulse. However, the calculation represents a 5.6 cm radius cathode and The electric field.3 and Current a 500 p3 laser pulse. Because emittance has densities scale similarly. unit3 of length tt scales linearly with A a3 well. The graphs show emittance normalized to the square l/2 root of the cathode area, A, (A - A 1. Variables whicn do not scale are the voltage and Current. Several simulations were performed with electrode with low laser intensity snapez based on Eq. (2), These calculations gave emit(
