We discuss
a compact source of intense terahertz radiation in which a low energy
electron beam travels close to a metallic grating. Spontaneous radiation
from such a device, known as the Smith-Purcell radiation [1], is too
weak to be of much practical interest. However, a Smith-Purcell device
can operate as a backward wave oscillator (BWO) when the group velocity
of the surface mode is in the direction opposite to that of the phase
velocity [2]. In a BWO, the optical power grows to saturation without
employing external mirrors if the beam current exceed a value known
as the start current [3]. Thus a Smith-Purcell device can generate high
optical power, although not via a large single pass gain speculated
by the Dartmouth group [4]. We have carried out a detailed analytic
study and numerical simulation of a simplified 2-D case, in which a
thin sheet of electron beam travels perpendicular to the grating grooves
and which is invariant under translation in the grove direction, taken
to be the y-direction [5]. As an explicit example we consider a system
in which the free space wavelength is 690 ?m, a rectangular grating
with period 173 ?m, the depth of the groove 100?m, the width of the
groove bottom 62 ?m, total length 1.3 cm, and the electron energy 30keV
correspondin to a velocity 0.35 times the light velocity. Assuming that
the electron beam is 10 ?m above the top surface of the grating, the
start current was found to be 50 A per meter in the y-direction. The
2-D results are then used to obtain conditions for oscillation in practical
3-D Smith-Purcell system [6]. Noting that the surface mode should be
freely propagating in the y-direction, we find that the optimum electron
beam is wide in the y-direction and thin in the x-direction perpendicular
to the grating surface, the emittance in the y- and x-direction being
respectively 20 mm-mrad and 0.03 mm-mrad. The start current is 40 mA
and optical power in the surface mode at saturation is 14 W. Out-coupling
of the power can be achieved in several ways; direct transmission out
of the grating entrance or by making use of the bunched electron beam
leaving the grating exit. Possible approaches to design the electron
gun are discussed based on line sources or by employing the flat beam
transform of a round beam [7]
[1] S.J. Smith and E. M. Purcell, Phys. Rev. 92 (1953) 1069
[2] H. L. Andrew and C. A. Brau, Phys. Rev. ST Accel. Beams, 7 (2004)070701
[3] Fundamentals of Microwave electronics
[4] J. Urata et al., Phys. Rev. Lett. 80(1998) 516
[5] V. Kumar and K.-J. Kim, submitted to Phys. Rev. E
[6] K.-J. Kim, V. Kumar, O. Kapp, and A. Crewe, in preparation
[7] R. Brinkmann, Y. Derbenev, and K. Floettmann, Phys. Rev. ST. Accel.
Beams 4 (2001)053501