
\chapter{Electron beam}\label{chapter_electron}

The performance of the photon source is dependent upon the
parameters of the electron beam in several important areas.
These parameters are listed in Table~\ref{elecprop}.  The first
column of numbers gives the set of parameters that have been adopted
as the design goals for the source.  These are the values that have
been taken as input in calculating the characteristics of the coherent
bremsstrahlung source.  The second column of numbers was
obtained from a concrete design of the \hd\ beam line~\cite{bldesign}
that was carried out by members of the Jefferson Lab Accelerator
Division. The exact choice of the final parameters has not yet been
made, but the preliminary design shows that all of the design goals
can be met within the available real estate.  The reduction of the
radiator-collimator distance from $80$\mlunit\ to $75$\mlunit\ does not
significantly affect the performance of the source.

\begin{table}
\begin{center}
\begin{tabular}{l@{\hspace{2cm}}c@{\hspace{1.5cm}}c}
\hline\hline
parameter & design goals & design results \\
\hline
energy & 12 \eunit & 12 \eunit \\
electron polarization & not required
& available \\
minimum useful current & 100 pA & 100 pA \\
maximum useful current & 3 $\mu$A & 5 $\mu$A \\
r.m.s.\ energy spread & $<10$ \Meunit & 7 \Meunit \\
transverse $x$ emittance & 10\mmlunit $\cdot\mu$r & 
10\mmlunit $\cdot\mu$r \\
transverse $y$ emittance & 2.5\mmlunit$\cdot\mu$r & 
2.3\mmlunit$\cdot\mu$r \\
x-dispersion at radiator & none & negligible \\
y-dispersion at radiator & none & $< 1$cm \\
$x$ spot size at radiator & 1.7\mmlunit\ r.m.s.\ & 
1.55\mmlunit\ r.m.s. \\
$y$ spot size at radiator & 0.7\mmlunit\ r.m.s.\ &
0.55\mmlunit\ r.m.s. \\
$x$ image size at collimator & 0.5\mmlunit\ r.m.s.\ &
0.54\mmlunit\ r.m.s.\\
$y$ image size at collimator & 0.5 \mmlunit\ r.m.s.\ &
0.52\mmlunit\ r.m.s.\\
distance radiator to collimator & 80 m & 75 m \\
position stability & $\pm$200 \micron & \\
\hline\hline
\end{tabular}
\end{center}
\caption
[Assumed and projected electron beam properties]
{Electron beam properties that were asked for (column 2) and
obtained (column 3) in a preliminary optics design for the
transport line connecting the accelerator to the \hd\ photon
source.}
\label{elecprop}
\end{table}


The following sections highlight the particular properties of the
electron beam which have a special impact on the performance of
the source.

\section{Beam polarization}

It has already been stated that to generate bremsstrahlung photons
with linear polarization it is necessary to use an oriented crystal
radiator.  However photons with circular polarization are produced
by ordinary incoherent bremsstrahlung any time the incident electrons
are longitudinally polarized.  In fact for $9$\eunit\ photons produced by
$12$\eunit\ electrons, the transfer from electron beam longitudinal
polarization to photon beam circular polarization is greater than $80$\%.
This raises the question of what happens when
one has longitudinally-polarized electrons incident on an oriented crystal
radiator.  What happens in this case is that the photon beam is
elliptically polarized; it carries both circular and linear polarization.
There is a sum rule that limits the sum of the squares of the linear
plus circular polarizations to be no greater than $1$.  Hence one sees
the linear polarization in coherent bremsstrahlung going to zero
as one approaches the end-point energy (see Fig.~\ref{polspec}) while
at the same time the circular polarization goes to $1$ at the end-point
(assuming electrons of $100$\% longitudinal polarization).

The statement in Table~\ref{elecprop} that electron beam polarization is not 
required for the \GX{} experiment in \hd{} is correct, but it is not
correct to assume that the photon source is independent of the state
of polarization of the electron beam.  The presence of a non-zero
circular polarization in the \hd\ photon beam will, in principle,
produce observable effects in the angular distributions measured
in photoproduction reactions.  This means that there will be an
important coupling between the \GX{} program and the other experimental
halls whose programs sometimes require them to have control over the
beam polarization.  This coupling can be eliminated by setting up
the tune of the electron beam line to \hd\ such that the longitudinal
component of the electron beam polarization is rotated to zero at
the crystal radiator.  Whether the decision is made to rotate it away
or simply to measure its value periodically, this consideration
underlines the importance of having a means to measure photon beam
polarization in a way that does not rely on {\em a priori} knowledge
of the properties of the electron beam.


Although the ability of the source to produce photon beams with both
circular and linear polarization complicates operation when one of
them is desired without the other, it does increase the versatility
of the source.  The two kinds of polarization are controlled
independently of one other, and together they give access to a more
complete set of polarization observables than would be possible
with only one or the other.


\section{Beam emittance}

The values for the electron beam emittances shown in Table~\ref{elecprop}
are estimates based upon the parameters of the current machine projected
to $12$\eunit \cite{bldesign}.  The definition of emittance used here is the 
product of the r.m.s.\ widths of the beam in transverse position and 
divergence angle. Because synchrotron radiation inside the accelerator occurs
mainly in the horizontal plane,
the emittance values in $x$ are generally larger than those for $y$.
The two vertical bends required for bringing the $12$\eunit\ beam
from the level of the accelerator up to beam height in \hd\ do increase
the vertical emittance a small amount over its value inside the machine;
this effect has been included in computing the vertical emittance shown
in Table~\ref{elecprop}.

The longitudinal emittance of the beam is important as it is the
limiting factor in determining the ultimate energy resolution of the
tagger.  The design goal of $0.1$\% photon energy resolution is well
matched to the energy spread expected for the \cebaf{} beam at $12$\eunit.


The place where transverse emittance plays a critical role is at the
photon collimator.  For optimum effectiveness in collimation it is
important that the virtual electron beam spot at the collimator position
be as small as possible.  The electron beam does not actually reach the
photon collimator, being bent into the dump by the tagger magnet
shortly after the radiator.
But considering the optics of the electron beam
as if the tagger dipole were switched off, the electron beam at the
radiator can be projected forward 
to form a virtual image on the collimator entrance plane.
The position and size of this virtual spot determines the 
definition of  $0^{\circ}$ emission angle for the photons.
If this spot is small compared to the collimator aperture and is
correctly centered then the bremsstrahlung photons of a given
emission angle $\alpha$ intersect the entrance plane of the
collimator in a well-defined ring of radius $D\alpha$ concentric
with the collimator aperture, where $D$ is the distance between the
radiator and the collimator entrance plane.  In this way a collimator
of diameter $d$ passes only those photons of emission angle $\alpha 
\le d/2D$.  
If however the size of the virtual spot is comparable to or
larger than the collimator aperture then the ring image of photons
of a given emission angle $\alpha$ is smeared out, so that the
effect of collimation is simply to reduce the intensity of the
beam but not to enhance the coherent component.

Note that this analysis does not place any specific limits on the
size of the beam at the radiator. The beam spot can and should be larger
there to increase the lifetime of the crystal between spot moves. For the 
SLAC coherent bremsstrahlung source the beam spot at the radiator was about 
$2$\mmlunit\ r.m.s. \  focused down to  a $1$\mmlunit\ r.m.s.\ virtual spot 
at the primary collimator positioned $91$\mlunit\ downstream of the radiator. 
 

The superior emittance characteristics of the \cebaf{} beam allow the
transverse dimensions to be somewhat smaller than this for the \hd\ source,
more so in the vertical than the horizontal dimension.  The difference
between the horizontal and vertical emittance of the \cebaf{} beam implies
that making the spot round at the radiator implies an elliptical 
virtual spot at the collimator, and \emph{vice versa}.  It is difficult
to construct a collimator with an elliptical aperture, so the choice
was made to make the virtual spot round.
This is why the beam spot on the radiator is asymmetric.

\begin{figure}
\begin{center}
\mbox{\epsfig{file=ch4_emittcuts.eps,width=\textwidth}}
\caption
[Coherent photon spectrum]
{Coherent photon spectrum for three different values of the 
electron beam transverse emittance.  The horizontal (shown on the
plot) and vertical emittances are assumed to scale together.  
A $3.4$\mmlunit\ collimator located $80$\mlunit\ from the radiator was
used for this calculation.}
\label{emittcuts}
\end{center}
\end{figure}

Figure \ref{emittcuts} shows how the collimated photon spectrum
depends upon the transverse emittance of the electron beam.  To generate
this plot the increases in emittance were simply translated into an
increased virtual spot size on the collimator.  This was done because
it was assumed that the spot size of the electron beam on the radiator,
already close to $2$\mmlunit\ 
r.m.s., cannot be further inflated and stay contained
within the limits of the crystal.  When the virtual spot size becomes
comparable with the collimator aperture then the collimation is rendered
ineffective, and the photon spectrum and polarization revert to their 
uncollimated values.  There is another connection between focal spot
size and beam emittance that is connected with the requirement that
all electrons enter the radiator at the same incidence angle with
respect to the planes of the crystal.  Practically, the divergence does
not broaden the coherent peak provided that it is kept below the mosaic
spread of the crystal.  A conservative
value for the allowable angular divergence $ \delta $
in the electron beam at the radiator would then be  $20\ \mu r$ .  Taken
together with a $500$\micron\ r.m.s.\ spot size at the focus, this leads to
an emittance of $10$\mmlunit $ \cdot \mu r$  at $12$\eunit.  
This corresponds to the upper curve in Fig.~\ref{emittcuts}.

\section{Electron beam line optics}

Translating the beam emittance into r.m.s.\ values for the
beam radius and divergence requires the knowledge of the $\beta$
function of the transport line between the accelerator and the radiator,
defined as the ratio of the beam size to its angular divergence.

The preliminary optics design~\cite{bldesign} of the \hd\ beam
line (see Table~\ref{elecprop}) is shown in Fig.~\ref{blattice}.  The
horizontal and vertical beta functions are shown in the upper and
lower panels, respectively.  Between the two panels is shown a schematic
of the transport lattice.  The design begins at the exit of the beam
from the end of the linac and ends at \hd.  The $z$ coordinate is
measured along the axis of the linac, with its origin at the mid-point
of the accelerator.  Fig.~\ref{benvelopes} shows the beta functions
translated into r.m.s.\ beam size and shifted to place the radiator
at the origin.  The design allows the ratio of the spot sizes at
the radiator and collimator to be adjusted over about an order of
magnitude simply by changing the current in the beam line elements.
In this way it will be possible to optimize the optics for a given
size of crystal and collimator after beams are delivered to the hall,
and more precise values for the emittances are in hand.


\begin{figure}
\begin{center}
\epsfig{file=ch4_betax.eps,width=4.5in}
\epsfig{file=ch4_blattice.eps,width=4.5in}
\epsfig{file=ch4_betay.eps,width=4.5in}
\caption
[Horizontal and vertical beta functions for electron beam]
{Horizontal (upper panel) and vertical (lower panel) beta
functions from the preliminary optics design for the transport
line from the accelerator to the \hd\ photon source.  The beam
line lattice is shown schematically between the two panels, with
dipole magnets represented by the short boxes and quadrupoles by
the taller lines.  The $z$ coordinate is equal to the flight path
length of the electrons starting at the center of the linac, up
to an error of a few cm from the vertical motion of the beam.
}
\label{blattice}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\mbox{\epsfig{file=ch4_bsize.eps,width=\textwidth}}
\caption
[Horizontal and vertical envelopes for the electron beam]
{Horizontal and vertical r.m.s.\ envelopes for the electron
beam in the region of the photon source, as derived from the
beam emittance and beta functions of Fig.~\ref{blattice}.
The origin of the $z$ coordinate has been placed at the radiator.
In the region between the radiator and the collimator the envelope
refers to the projected image of the electron beam, and does not
describe the size of a physical beam that exists in that region.}
\label{benvelopes}
\end{center}
\end{figure}

Not only must the virtual electron spot be small enough to fit within
the collimator aperture, but it must also be centered on the aperture
and stable.  In order to maintain a stable beam position on the
collimator, the SLAC experiment \cite{Kaune} instrumented the 
collimator with a secondary-emission detector.  The detector was
of the ``pin-cushion'' design and was installed between segments of the
collimator near the position of the shower maximum.  The readout was
divided into four quadrants, which read equal currents when the beam
was properly aligned on the collimator.  The readout was connected via
a feedback loop to the last steering elements on the electron beam line
prior to the radiator.  Over that distance a bend of only $10\ \mu r$
results in a shift of $1$\mmlunit\ at the collimator position.
The small deflections that are necessary to keep the beam centered
on the collimator do not produce appreciable walk in the beam-crystal
angle. This means that an active feedback system can be set up
between the instrumented collimator and deflection coils just
upstream of the radiator, that can operate independent of the
crystal alignment system to keep the electron beam
aimed at the center of the collimator.

The experimental
program in parity violation at Jefferson Lab has already demonstrated
a position stabilization circuit that is able to keep the beam position
steady to within $20$\micron over a $20$\mlunit\ lever arm.  
A less sophisticated version of this circuit will meet the position
stability requirements for the \hd\ photon source.

\section{Electron beam dump}

The electron beam is dumped in the horizontal plane, as shown in
figure \ref{photon_line}.  The horizontal bend offers several
advantages over dumping the beam into the ground.  The tagger magnet
is easier to support if it sits in the horizontal position.  It is also
easier to mount and service the focal plane in this position.  The
dump itself is also more accessible in case it needs to be serviced.
An above-ground dump also affords the possibility of running parasitic
beam dump experiments that do not interfere with the operation of the
experimental hall.

The primary design requirement for the electron beam dump is that it
has a sufficiently high capacity to handle beams of the highest
intensities foreseen for the \GX{} experiment in \hd. A $60$\kpwunit{} design 
would provide a a healthy margin for operation of a $12$\eunit\ beam at 
$3$\miamps{} and sufficient capacity to handle $3$\miamps at $20$\eunit\ in 
the case of a further upgrade.



\section{Beam containment and shielding}

There are three factors that must be taken into account in the
design of the shielding for the \hd\ beam line.  The first is
the constraint on the background radiation level that is allowed 
outside the beam enclosure.  The second factor is the
level of radiation in the experimental hall which can generate
background in the detector during normal running.  The third factor
is the control of hazards which may occur in the event of a failure
of one or more of the beam delivery systems.  
The first issue has been studied by the Jefferson Laboratory Radiation
Controls Group, and will be discussed further in the chapter on Civil
Construction.  The latter two considerations have been  studied by
a working group headed by L.~Keller (SLAC).  A summary of their
recommendations~\cite{Keller1} follows.



Assuming that the electron beam dump is shielded to the requirements
of radiation safety, the next source of background radiation in the
experimental hall is the photon collimator.  The most penetrating
forms of radiation from the collimator are muons and neutrons.  A
Monte Carlo simulation, assuming a $13$ radiation lengths tungsten
collimator followed by a sweeping magnet and $5$\mlunit{} of iron shielding,
predicted a flux of $1.4\times 10^3 \mu$/s incident on the detector
at full operating beam intensity.  This is a negligible rate
compared with the trigger rate from photon interactions in the
target.  The flux of neutrons from the collimator is more difficult
to calculate, but some fraction of $1$\mlunit{} of concrete shielding will be
needed surrounding the collimator enclosure to shield the hall from
energetic neutrons.



With regard to hazards associated with the accidental failure of
beam line elements or controls, the following measures were
recommended in the Keller study~\cite{Keller1} and have been
incorporated into the \hd\ design.  The dipole string that bends
the electron beam up towards the surface from the below ground
and then bends it back horizontal will be connected in series
so that failure of a magnet supply or current control electronics
cannot result in the beam being steered into the ceiling of the
tagger building.  The power supply feeding this string of magnets
will be protected by a meter relay that shuts off if the current
varies from its desired value outside a predefined tolerance.  A
similar meter relay will also be used on the power supply of the
tagger magnet.  An electron beam collimator with a burn-through
monitor will be located just upstream of the radiator to prevent a
mis-steered beam from using radiator support structures as a
bremsstrahlung target.
Permanent magnets will be located in the upstream region of the
photon beam line to bend an errant electron beam into the ground
in the case that beam is present while the tagger magnet is off.
An emergency beam stop will be installed in the bottom of the
photon beam line to catch the errant beam deflected
by the permanent magnets.  It will be equipped with a current monitor
to shut down the primary beam any time electrons are sensed in the
photon beam line.  Ion chambers located upstream of the photon collimator,
and also  at the entrance to the photon beam dump behind the experiment,
will monitor the total flux in the photon beam and shut off the beam
if the flux exceeds a safe value.

