Fig. 1-9 A schematic diagram of the phase distribution of a beam, where the abscissa denotes the longitudinal beam position (z) and the ordinate denotes the corresponding momentum (Pz) The phase space is divided into several domains in the spatial direction, and for each domain the beam momentum is controlled so that the average momentum becomes zero.

Fig. 1-10   Decrease of the phase space volume of the charged particle beam by the laser beat-wave cooling method N denotes the circulation number of the beam. The phase space volume of the beam rapidly decreases with increasing circulation number, so the beam is cooled.

Though the main objective of an accelerator is to increase the energy of a charged particle beam, it is equally important to get a beam of high quality by controlling the beam distribution in the beam phase space (the space consisting of the configuration space and the momentum space of the beam). We are studying the physics and technology of the control of charged particle beams in general, and in particular we consider it very important to establish a good beam "cooling" method, i.e., a method to reduce the dispersions of the energy and the direction. Because the dispersions in the energy and the direction of motion of the beam particles are interpreted as "heat," a beam which has low dispersion is considered to be "cold." In order to produce an electron beam with uniform energy we devised a new beam cooling method, a "laser beat-wave cooling method," and confirmed by computer simulations that this new method is effective. The stochastic beam cooling method is a representative one of the active cooling methods, where the internal fine structure of a beam is measured and the beam is feed-back-controlled using this information. This method is effectively used in experimental research, but the information on the positions of the particles to be controlled also contains information of a large number of surrounding particles, and therefore the cooling effect is statistical, and consequently, inefficient. Moreover, because of certain other complications, this method cannot be applied directly to the cooling of an electron beam. In the newly proposed method, at first, the "center of balance of the velocity distribution" of the beam particles is measured spatially. Next, we calculate the necessary wavelength components of a multi-wavelength laser, so that the spatial structure of the beat wave produced by the interference of the laser with the undulator magnetic field (the spatially oscillating external magnetic field) cancels that of the velocity distribution of the beam, and the beam energy becomes uniform (Fig. 1-9). We confirmed by computer simulations that the phase space volume of the beam decreases rapidly with this method (Fig. 1-10) and the phase space volume of the laser increases correspondingly.

Reference Y. Kishimoto et al., Phase Space Control and Consequence for Cooling by Using a Laser-Undulator Beat Wave, Phys. Rev. E, 55, 5948 (1997).

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