W.H.C. Theuws, J.I.M. Botman, H.L. Hagedoorn, R.W. de Leeuw,
C.J. Timmermans
Eindhoven University of Technology, Cyclotron Laboratory
P.O. Box 513, 5600MB Eindhoven, The Netherlands
The 10 - 75 MeV Racetrack Microtron Eindhoven (RTME) is designed to serve as injector for the electron storage ring EUTERPE. In RTME electrons are injected at 10 MeV by a travelling wave linac. The microtron's 5 MeV standing wave cavity, which is synchronized with the linac, accelerates the electrons 13 times. The main RTME magnets are two-sector magnets, which are tilted in their median planes, to provide strong focusing forces for optimal electron optical properties. Closed orbit conditions are fulfilled with the help of small correction dipoles located in the microton drift space; these dipoles are adjusted on the basis of beam position measurements. Isochronous acceleration is accomplished by position and phase measurements. An elaborate diagnostic system will be used for efficient commissioning of the combination of the 10 MeV linac and RTME.
A 10 - 75 MeV racetrack microtron (RTME), which is shown in figure 1, has been chosen as injector for the 400 MeV electron storage ring EUTERPE [1], because a microtron offers a beam with small energy spread at low RF requirements. In RTME electrons are injected by a totally revised 10 MeV travelling wave
linac (type M.E.L. SL75/10). The microtron's 5 MeV standing wave cavity, which is synchronized with the linac, accelerates the electrons in 13 times to their extraction energy of 75 MeV [2].
The design of the microtron is basically dictated by the two resonance
conditions.
First, the revolution time of the first orbit, 
, is an
integer multiple, 
, of the RF-period 1/f ( 
).
Second, each revolution time must exceed the preceding one by another
multiple ( 
).
From these resonance conditions two basic relations for a racetrack microtron
are derived:
and
where 
is the injection energy, L is the
field-free region between the magnets and 
is the resonant or
isochronous magnetic field, corresponding to the energy gain per turn,
The maximum energy is given by 
with N the
number of cavity passages.
The RF-frequency of the RTME cavity, f, must be the same as the
RF-frequency of the 10 MeV linac.
The mode number, 
, and the number of orbits, N, should be as small
as possible to maximize the phase acceptance and to minimize phase errors due
to imperfections of the construction [3].
The field-free region must be large enough to place the microtron's
cavity.
As we want to use normal conducting magnets, the magnetic field strength in
the air gaps is limited by the maximum field strength in the iron (about 2 T
for ordinairy steel).
The basic parameters that have been chosen for RTME are summarized in
table 2.
The main bending magnets of RTME have two magnetic field sectors to provide
strong focusing forces.
Sector 1 and 2 have magnetic field strengths of 
and 
, respectively.
The trajectories in the bending magnets consist of two circular arcs, defined
by their centres 
and 
, radii 
and 
and
angles 
and 
, respectively (see
figure 2).
The tilt angle, 
, is retrieved from geometrical considerations:
The magnetic field is to be chosen:
such that resonant acceleration is not violated.
The parameters a and 
, not prescribed so far, determine the
focusing properties of RTME.
Therefore, the transversal acceptance of RTME has been calculated for many
combinations of a and , where estimations for the fringing
fields of the bending magnets with their field clamps have been taken into
account [4].
Consequently, a = 1.17 and 
have been chosen, which
give a horizontal and vertical acceptance of 40 mm 
mrad and
10 mm mrad, respectively.
With eq.(3) this yields 
.
Figure 3: Trajectories in the horizontal and vertical plane for a parallel beam and for a divergent beam at injection. Homogeneous option: (a) x0 = -1..+1 mm, x'0 = 0, (b) x0 = 0, x'0 = -1..+1 mrad, (c) z0 = -1..+1 mm, z'0 = 0, (d) z0 = 0, z'0 = -1..+1 mrad. Two-sector option: (e) x0 = -1..+1 mm, x'0 = 0, (f) x0 = 0, x'0 = -1..+1 mrad, (g) z0 = -1..+1 mm, z'0 = 0, (h) z0 = 0, z'0 = -1..+1 mrad [2].
The racetrack microtron with two-sector bending magnets has been compared with a microtron with homogeneous magnets. For both types of microtrons the trajectories in the horizontal and vertical plane are plotted both for a parallel and a divergent beam at injection (see figure 3). The main difference is the periodicity of the betatron oscillations.
For the horizontal plane motion the tune of the two-sector option is 1.15 for the first and 1.07 for the final orbit. For the homogeneous option these numbers are 1.10 and 1.04, respectively. This leads to a smaller beam size in case of the two-sector magnets.
The stronger focusing would also lead to smaller vertical beam sizes if the defocusing of the fringing fields would be less. However, the fringing fields lead to a blow-up of the beam in the first turn (the trace of the matrix is larger than 2 [5]). The tune of the two-sector option is 0.22 for the second and 0.30 for the final orbit. For the homogeneous option these numbers are 0.09 and 0.05, respectively.
Because of the strong focusing forces provided by the main bending magnets
RTME operates further from integer resonances than conventional microtrons.
Therefore the sensitivity for misalignments of the bending magnets is
smaller.
It has been investigated that all alignment tolerances can be met by
mechanical alignment except for the tilt angle, .
Furthermore, the magnetic field maps of the main bending magnets have been
measured.
These field maps have been used for numerical orbit calculations, which have
shown that it is not possible to obtain 
bends for all orbits,
simultaneously.
However, the effects of the alignment error of the tilt angle as well as the magnetic field imperfections can both be counteracted by an array of correction dipoles that is located in the field-free region halfway the two dipoles.
An elaborate diagnostic system will be used for efficient commissioning of the combination of the 10 MeV linac and the 10 - 75 MeV racetrack microtron [6]. The commissioning will take place in two stages.
In the first stage the cavity will be replaced by a temporary beamline with a quadrupole and an OTR-set-up, which are used to measure the shape of transversal emittances [7]. Consequently, the emittance of the injected beam can be matched to the calculated acceptance of the microtron by adjusting the quadrupoles in the beam guiding system between the 10 MeV linac and RTME [8].
In the second stage the combination of the linac and RTME will further be assembled. Then the energy of the injected electrons, the cavity potential and the phase difference between the accelerating voltage of the linac and the cavity are adjusted. The energy of the beam is measured by means of the left RTME bending magnet, see figure 4. This is done for several different positions of the phase-shifter, which determines the phase difference of the accelerating voltage between the linac and the RTME cavity. Consequently, the energy will appear as a sine-like function of the position of the phase-shifter:
where 
is the energy of the injected beam, 
is the
cavity potential and 
is the phase difference between linac and
cavity.
The mean of this function is the injection energy; the amplitude of the
harmonic part is the cavity potential.
Further, the measurement yields a calibration for the phase-shifter.
In the microtron many stripline beam position monitors (BPM's) are used to adjust the array of correction dipoles discussed in the previous section [9]. A phase-probe measures the phase difference between the cavity voltage and the first harmonic of the electron bunches in the field-free region of the microtron. This phase-probe can be placed in each of the twelve orbits. The phase-measurements as well as the beam position-measurements are used to optimize the adjustable microtron parameters.
