Abstract
The phenomenon of radial beam break-up observed in terms of long, multi-section electron linear accelerators has been analyzed using a multi-cavity model. In this model the source of regeneration due to backward wave amplification is ignored. The dominant phenomenon involves build-up of radial modes in each cavity as coupled by the electron beam. The resulting differential equations are integrated by the method of steepest descent and by a numerical iteration method. Scaling laws in terms of the pulse length, beam intensity, energy gradient, and length of the structure are derived.
Highlights
In this paper we will give the theory of the second mechanism only, which is the dominant cause of the beam break-up (BBU) phenomena occurring at SLAC
We will assume: (a) Only one resonant mode at a frequency w0 and loss factor Q is of significance. (b) The cavity has axial symmetry and the axial electric field vanishes along the axis of symmetry. (c) The rate of build-up of oscill.ation giving rise to the radial modulation of the beam is small compared to w 0’ th Consider a particle of charge e to cross at a t.ime t the n of N cavities at a distance x from the z-axis, taken to be an axis of symmetry
Equation of Motion Let the electric field F in the n th cavity be derivable from a vector potential
Summary
The observed beam current of the SLAC SGO-section linac appears to obey the results of independent particle dynamics at low intensities. As was first observed on April 24, 1966, the pulse length of the transmitted beam appears to shorten provided the beam current exceeds a threshold value at a given distance along the accelerator; the g-rester the distance, the lower the threshold. The first mechanism discussed in the above references results from the negative group velocity of the TEMll mode of the conventional disk-loaded structure This negative goup velocity will feed transverse energy from the end of a given acceleratin, m section t.o the front, leading to the regenerative action involved in the “backward-wave oscillator. This mechanism is very gcncral, being quite independent of the d&ailed. structure of the accelerating sections
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