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Acceleration using total internal reflection

07 Jun 1991-
TL;DR: In this article, the authors examined the functional dependence of the electromagnetic fields above the surface of the dielectric for polarized incident waves and presented an experimental arrangement for testing the performance of the method, using apparatus under construction for the Grating Acceleration experiment at Brookhaven National Laboratory.
Abstract: This report considers the use of a dielectric slab undergoing total internal reflection as an accelerating structure for charged particle beams. We examine the functional dependence of the electromagnetic fields above the surface of the dielectric for polarized incident waves. We present an experimental arrangement for testing the performance of the method, using apparatus under construction for the Grating Acceleration experiment at Brookhaven National Laboratory. 13 refs., 4 figs., 2 tabs.

Summary (1 min read)

1 Introduction

  • There must be a reflected wave inside the dielectric that makes an equal angle with respect to the surface normal.
  • Thus the electric field of the reflec^d wave can be written.

Reflected wave

  • The solution of the set of equations gives 6 complex expessions for the components of the reflected wave.
  • The magnitudes of the magnetic field components are Hex -Hi sin* EQUATION H/g =.
  • Hi cos* with respect to the incident wave.
  • The total electric field has the magnitude E 0 L as expected and each of the components also has the phase 2 with respect to the incident wave.
  • The magnitudes of the electric field components are.

Transmitted wave

  • The magnitudes of the surface electric field components are The x and z components of the magnetic field components have the phase (T + n/2j.
  • It thus appears that the peak surface accelerating field enhancement will always be less than 2.
  • Measured quantities should include the strength of the acceleration gradient, transverse forces, sensitivity to the direction and polarization of the incident wave, and the breakdown strength of the dielectric medium.
  • The analysis spectrometer following the interaction chamber will use point to point focusing in the bend (x-z) plane.
  • The F^ force changes the particle's momemtum so the dipole in the spectrometer will spread the trajectories accordingly in the x direction.

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BNL—52290
DE91 016612
ACCELERATION
USING TOTAL INTERNAL REFLECTION
R.C. Fernow
7 June 1991
CENTER FOR ACCELERATOR PHYSICS
PHYSICS DEPARTMENT
BROOKHAVEN NATIONAL LABORATORY
ASSOCIATED UNIVERSITIES,
INC.
UPTON,
LONG ISLAND, NEW YORK 11973
_

ACCELERATION USING TOTAL INTERNAL REFLECTION
R.C.
Fernow
Brookhaven National Laboratory
This report considers the use of a dielectric slab undergoing total
internal reflection as an accelerating structure for charged
particle beams. We examine the functional dependence of the
electromagnetic fields above the surface of the dielectric for
polarized incident waves. We present an experimental arrangement
for testing the performance of the method) using apparatus under
construction for the Grating Acceleration experiment at Brookhaven
National Laboratory.

CONTENTS
1. Introduction 1
2.
Wavevector relations 2
3. Polarization of the incident wave 4
4.
Solution for incident wave with Hy
1
= 0 5
5. Solution for incident wave with Ey
L
= 0 8
6. Forces 11
7.
Practical considerations 14
Endnotes and references 17

TOTAL INTERNAL REFLECTION / 1
1 Introduction
Methods for using the very large electric fields in laser beams for
accelerating charged particles have been under investigation for
many
years[l-4].
In one class of method the particles interact with
slow, evanescent waves set up on the surface of an accelerating
structure. This method is closely related to that employed in disk
loaded linacs powered by RF sources!5]
.
The axially symmetric
cavity fields can be considered as the infinite sum of surface
fields.
Examples of this technique explicity using external laser
beams include acceleration over a metallic grating or acceleration
over a dielectric slab undergoing total internal reflection.
The phenomenon of total internal reflection is a well known subject
in physical
optics[6-9].
Consider a boundary surface with a
dielectric of refractive index n on one side and vacuum on the
other.
Let a plane wave be incident on the boundary from the
dielectric side. The wave will be totally reflected back into the
dielectric provided the angle 0 with the surface normal exceeds the
critical angle €» given by
sin8
c
= (1)
However, the solution of the Maxwell equations requires that an
evanescent wave exist on the vacuum side of the boundary surface.
The possibility of using the surface fields on a dielectric
undergoing total internal reflection to accelerate particles was
apparently first suggested by LohmannflO] in 1962. He apparently
realized that the accelerating field vanishes for relativistic
particles in a geometry where the incident wave does not have a
component perpendicular to the trajectory of the accelerated
particle.
We will call this the classical geometry, since it is the
one that is customarily employed in discussions of total internal
reflection.
The subject has been actively studied by a group at the Yerevan
Physics Institute[11-12]. Kheifets[13] gave explicit expressions
for the transmitted field components for the case of the classical
geometry. He showed that the solutions could be broken into the two
cases depending on the polarization of the incident wave. He also
studied the conditions for stability for elliptically polarized
waves.
He found that a net force exists normal to the boundary
surface and suggests cancelling it using an external magnetic
field. Nagot-sky et al[14] showed that the synchronism condition
between the incident wave and a particle travelling along the

TOTAL INTERNAL REFLECTION / 2
surface is equivalent to the condition for Cerenkov radiation. They
showed that phase stability required a second magnetic field
oriented normal to the particle trajectory and to the dielectric
surface.
There have been a number of reviews of new acceleration techniques
that also consider the possibility of using total internal
reflection^, 11,12,15] .
2 Wavevector relations
Consider the coordinate system shown in Fig. 1. The x-z plane
represents the boundary between a region with dielectric constant
n (y < 0) and free space (y > 0). The normal vector to the boundary
surface lies along the y direction. A plane wave k
1
is incident
from the dielectric side. The angle 9 is the polar angle between k
1
and the +y direction, while the angle $ is the azimuthal angle
between the projection of k
1
on the x-z plane and the -x
axis.
Fig.
1 Coordinate system
Our goal will be to produce suitable electromagnetic field
configurations in order to accelerate a particle along the z
direction.

Citations
More filters
Patent
09 May 2013
TL;DR: In this article, the total reflection of electromagnetic pulses with a frequency falling into the THz frequency domain that utilize the evanescent filed for the acceleration of electrically charged particles.
Abstract: The invention relates to a such particle accelerator setup (1, 11 ) and method based on the total reflection of electromagnetic pulses with a frequency falling into the THz frequency domain that utilize the evanescent filed for the acceleration of electrically charged particles. Said setup includes a radiation source (5) to emit high-energy THz-pulses, preferably comprising a few optical cycles, having a large peak electric field strength, as well as two optical elements (2, 12) in the form of a pair of bulk crystals made of a substance that exhibits large refractive index, low dispersion and high optical destruction threshold, wherein said optical elements are transparent for the THz radiation. The inventive solutions represent much simpler, more compact and more cost effective alternatives compared to the prior art particle accelerator setups.

6 citations

Journal ArticleDOI
TL;DR: In this article , a general solution of the excitation problem of a symmetric flat dielectric structure by two laser pulses is obtained, and the effect of the asymmetric part on the total amplitude of the accelerating and defocusing fields is also analyzed.
Abstract: General solution of the excitation problem of a symmetric flat dielectric structure by two laser pulses is obtained. The symmetrical geometry consists of two dielectric prisms separated by a vacuum channel for electron acceleration (so called “sandwich”). Each prism can be illuminated with a separate laser pulse; electric filed amplitudes of pulses can differ. The general solution consist from a symmetric distribution and asymmetric one of a longitudinal electric field across the vacuum channel. In the case of a general solution, the effect of the asymmetric part on the total amplitude of the accelerating and defocusing fields is also analyzed. We determined also conditions when a symmetric or asymmetric solution only is realized. For these cases, the obtained analytical solutions are compared with results of full time-domain numerical simulations of bilateral excitation of dielectric prisms with laser pulses.