A comparative study of RF and induction linac approaches to phase rotation of a muon bunch in the production region of a {mu}{sup +}- {mu}{sup {minus}} collider Page: 5 of 7

completed the energy spread is partially regenerating as the
beam moves along. Due to the head-to-tail energy variation,
the length of the beam pulse changes as it propagates through
the phase rotation linac. The transverse energy is a significant
fraction of the total energy and needs to be taken into account
when analyzing the longitudinal propagation of the pulse.



Fig. 3: Nor
The detai
been previot
be repeated*
of the RF an
out and on w
Pions are
pulses impin
peaking in th
study we the
50 to 250 M
energy inter
spread in the
= 0.5*L. Fo
half a wave
within a wav
of the target
f - 100 MII
- 5 nsec. For
swing AB a
hysteresis l
Metglas 260
and hysteres
cAt - 40 m:
80 m from t
length is - 1
The acc
maximum e

determined by the Kilpatrick criterion relating Eoax in the
accelerating gap to the RF frequency f[4],
f(MHz) = I.64EK(MV / m)e EK(AIV/m) (1)

and the enhancement factor by which the Kilpatrick field can
be safely exceeded. The enhancement factor is a function of
pulse length and is - 2 for pulse lengths 50 to 200 sec [5]
which spans the cavity fill times of interest for this study- For
the three frequencies f = 30, 50 and 90 MHz chosen for the RF
linac solution, the corresponding two times Kilpatrick fields
are 15, 19.8 and 21.8 MV/m. The acceleration gradients
averaged over the full cavity length were then calculated by
SFISH giving 2.1, 3.3 and 4.2 MV/m for the particular cavity
geometries that were specified. The practical gradient for the
lowest frequency case doesn't simply scale from the other two
and the Kilpatrick fields because in this case a folded cavity
geometry was chosen to reduce the cavity diameter, and this
0 2 4 6 8 10 causes some enhancement of surface field relative to average
field strength in the gap.
oT The accelerating gradient in the induction linac is limited
malized Fourier transform of the cavity voltage. by consideration of the properties of the induction core,
.s of the two approaches to phase rotation have dielectric breakdown, vacuum insulator surface flashover and
sly described [1,2] and for the most part will not vacuum breakdown. Details of the analysis are in ref. [2].
here. Instead we will concentrate on comparison Since voltage rise time requirements are relatively relaxed,
d induction linac solutions that have been worked t - 50 nsec, the induction cores and the vacuum insulators
hy they turned out the way they did. were stacked vertically to maximize accelerating gradient. The
gradient limiting factors were then insulator flashover and
II. DESIGN CONSTRAINTS vacuum breakdown. For pulse duration - 100 nsec, the
produced by at = 1 nsec 10 to 30 GeV proton insulator surface flashover field strength was taken to be
ging on a target and have kinetic energy spectra 50 kV/cm and the vacuum breakdown field 100 kV/cm. For
he range 100 to 200 MeV. For purposes of design induction cells occupying 40% of the axial length of the
refore chose a pion/muon kinetic energy interval accelerator the practical gradient was found to be - 1 MV/m.
eV for phase rotation. As the pions/muons in this If the breakdown limiting field strengths are increased by 50%
val propagate a distance L from the target the then the flux core would limit the practical gradient to
ir arrival times increases roughly according to cAt _ 1.5 MV/m. In summary the realizable accelerating gradients
r the RF approach cAt should not exceed about are two to three times higher in the RF linac than in the
length so the highest frequency cavities should be induction linac approach to phase rotation.
length L - X of the target, or within 2 - 3 meters For 2x1013 muons per pulse, the peak beam current in the
if the size of cavities is to be reasonable (say induction linac is less than 100 A and far less than the
z). The corresponding beam pulse lengths are induction core leakage current - 3.5 kA so waveform
the induction linac, cAt is determined by the flux distortion due to beam loading is negligible and does not
nd the maximum B that can be tolerated for introduce any design constraints. Furthermore because of the
)ss in the induction cores; cAt = c . . For relatively low beam current and a large beam tube radius
Bmax of 15 cm, beam breakup instability is not a concern in the
5SC, which has high saturation flux (AB = 2.5 T) induction linac,
is losses measured up to 5max - 20 T/ sec [3],
so the induction cavities should be placed about
he production target and the corresponding pulse
25 nsec.
elevating gradient in the RF linac is limited by the
electric field strength before breakdown. This is


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Turner, W. C. & Kirk, H. G. A comparative study of RF and induction linac approaches to phase rotation of a muon bunch in the production region of a {mu}{sup +}- {mu}{sup {minus}} collider, article, October 1996; California. (https://digital.library.unt.edu/ark:/67531/metadc688227/m1/5/ocr/: accessed August 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.

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