ACCELERATOR PHYSICS ISSUES FOR FUTURE ELECTRON ION COLLIDERS. Page: 3 of 5
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at their limits, the only way to raise the luminosity is to
increase the collision frequency Fe, by increasing Ill, the
number of bunches. One constraint on M is the maximum
average current. Another is the need for a minimum bunch
spacing - perhaps due to the electron cloud effect, or due to
a minimum reset time for detector electronics. In an elec-
tron ring the average current may be limited by the total
synchrotron radiation load, or by the heat load per meter. In
a superconducting ion ring the beam image current which
flows in the vacuum chamber walls is a resistive heat load
at cryogenic temperatures. A maximum average cryogenic
heat load of about 1 W/m can be tolerated, to stay within
the capacity of typical cryogenic systems. Beam Position
Monitor signal cables may suffer unacceptably large cold-
to-warm heat loads, due to resistive heating by the signal
current, when the number of bunches becomes large and
the bunches are too short .
3 ION STORAGE RING ISSUES
Long range beam-beam. It is relatively easy to im-
munize an electron ion collider against parasitic long range
beam-beam interactions, by arranging for the early separa-
tion of the two beams (with very unequal rigidities). For ex-
ample, in eRHIC the beams begin to be magnetically sep-
arated at only 9.8 meters from the IP, before entry into the
first quadrupole, and after only one parasitic interaction.
Electron cloud effect. Electrons produced by ioniza-
tion of the residual gas are accelerated by the electrical
field of the next passing ion bunch, eventually hitting the
vacuum chamber wall and emitting secondary electrons.
This process can runaway if the bunches are spaced too
closely, driving a large cryogenic heat load in a supercon-
ducting ion ring and perhaps causing instabilities. The ef-
fect has been much studied for the LHC, where the nom-
inal bunch spacing is 25 ns and there are nominally about
1011 protons per bunch [11, 12, 13]. In fixed target mode
the Tevatron routinely operates with 1008 bunches of ap-
proximately 2 x 101) protons, spaced by about 18.9 ns (53
MHz), without undue cryogenic difficulty. Bunch gaps -
such as the 1 is abort gap in the Tevatron - act to clear the
electron clouds. Unfortunately there is a paucity ofhard ex-
perimental data from existing cryogenic accelerators with
closely spaced bunches, although the normal conducting
SPS is generating interesting data with LHC bunch loading
parameters. This problem needs more investigation, espe-
cially in making careful measurements on cryogenic stor-
age rings - HERA, RHIC, the Tevatron - and in the SPS.
Intra-Beam Scattering (IBS) and electron cooling.
Intra Beam Scattering diffusion can be very strong for
heavy ions such as gold. For example, in RHIC the nor-
malized emittance is expected to grow from about 2 pm to
about 7 pm in a ten hour store with 10' ions per bunch.
As a rule, the effect is stronger at lower energies. Electron
coolers can fight IBS, even reducing the emittance below
its injection value. For example, the RHIC gold emittance
is predicted to shrink to about 1 pim after 1 hour in a pro-
posed e-cooling upgrade scheme [14, 15].
Laslett space charge tune shift. The space charge
tune shift of the ion beam is given by
Although its dependence on N/e is reminiscent of the
beam-beam parameter, in contrast is the strong dependence
on ring circumference C, RMS bunch length a ., and the
Lorentz factors ;3 and ;. Because the space charge inter-
action is "smoothly" spread over the circumference of the
ring, resonances tend to be only weakly driven, and so val-
ues as large as AQ, - 0.1 can reasonably be supported.
At constant bunch length space charge is much more of a
problem at injection, when :3i2 is smallest. However, it is
possible to make the bunch much longer at injection. For
example, eRHIC injects and accelerates with a 28 MHz RF
system, but stores beam for collisions with a 197 MHz RF
system. In collision the bunch length cannot be increased
beyond about aT - 3* without the loss of luminosity to
the "hourglass" effect.
4 ELECTRON STORAGE RING ISSUES
Synchrotron radiation. The synchrotron radiation en-
ergy loss per electron per turn of a storage ring with dipoles
of bending radius p is
E ' [GoV ']
U0 [MeVI = 0.0885 E [Gll
and the total power radiated is
P [ =W] - U( [IleV] I [A]
One constraint on the maximum beam current in the SLAC
B-Factory High Energy Ring (HER) is the need to keep the
linear heat load per meter of dipole, given by
to less than about 15 kW/m [9, 16]. The HER serves as a
natural "ruler" against which to compare prospective elec-
tron ring parameters. For example, Table I shows that, with
360 bunches, the eRHIC bunch spacing of 35.5 ns is mod-
est by comparison with the HER, which has as many as
1658 bunches, with a bunch spacing as small as 4.2 ns.
Thus, the synchrotron power and linear power in the arcs
are much less in the eRHIC ring than in the HER.
Polarization. The natural Sokolov-Ternov polariza-
tion time for electrons stored in a ring is
TaI [s] = 1.8 
E, [GcV ]
AQ, t r
fi tor4-*3 1 2(2;r),
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PEGGS,S.; BEN-ZVI,I.; KEWISCH,J. & MURPHY,J. ACCELERATOR PHYSICS ISSUES FOR FUTURE ELECTRON ION COLLIDERS., article, June 18, 2001; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc723383/m1/3/: accessed April 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.