Field Distribution of a Planar Electrostatic Wiggler and Modulation Effect on the Motion of Relativistic Electrons
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Field Distribution of a Planar Electrostatic Wiggler and Modulation Effect on the Motion of Relativistic Electrons Shi-Chang Zhang
Received: 24 June 2009 / Accepted: 1 October 2009 / Published online: 14 October 2009 # Springer Science + Business Media, LLC 2009
Abstract A planar electrostatic wiggler is formed by two parallel metallic plates, where the upper-plate is corrugated with sinusoidal ripples and connected to a negative voltage and the lower-plate is smooth and grounded. The field distribution is mathematically derived in detail. It is demonstrated that this planar electrostatic wiggler can efficiently modulate the motion of relativistic electrons just as a magneto-static wiggler does in a free-electron laser. Results obtained here will provide basis to analyze the amplification mechanism of a fast wave by a relativistic electron beam in a planar electrostatic wiggler. Keywords Planar electrostatic wiggler . Modulation effect . Relativistic electrons
1 Introduction The free-electron laser (FEL) is a new kind of coherent radiation source [1–10]. Compared to the ordinary lasers, it has peculiarities such as high efficiency, powerful output, and tunable frequency from microwave to x-ray, especially in far-infrared range [11]. Physically speaking, it is based on the coherent radiation stimulated by relativistic electrons which are immerged in a wiggler. The so-called wiggler is a magneto-static system, where the magnets are alternatively arranged so as to let the magnetic field have a sinusoidal distribution. Relativistic electrons are modulated by this magnetic field and move along approximately sinusoidal trajectories. The wiggler provides coupling of the electron motion with the electromagnetic wave mode and pumps the kinetic energy of electrons to the wave, which results in the coherent amplification of the wave [1]. After the pioneer operation of the free-electron laser at Stanford University [2], two other types of wigglers were proposed, which were expected to play similar role as a magneto-static wiggler does. One is the electromagnetic-wave wiggler, where the components of the wave S.-C. Zhang (*) Institute of Photoelectronics, School of Information Science and Technology, Southwest Jiaotong University, Campus Mail Box 50, Chengdu, Sichuan 610031, People’s Republic of China e-mail: [email protected]
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J Infrared Milli Terahz Waves (2010) 31:249–258
have sinusoidal variation in space and time and govern the relativistic electrons [12]. The other is the electrostatic wiggler either by using a ring-loaded waveguide where the rings are insulated from each other and alternatively connected to a positive/negative voltage [13], or by utilizing a large potential drop of the electron beam to the wall corrugated with ripples [14]. The advantage of a magnetic wiggler compared to an electromagnetic-wave wiggler and an electrostatic wiggler is related to practical feasibility of large magnetic field amplitudes. In fact, on axis the force acted by a magneto-static wiggler field on an electron is evz
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