FREE ELECTRON LASERS AND HIGH-ENERGY ELECTRON COOLING. Page: 4 of 10
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while maintaining its ultimate luminosity constant .
Reduction of the electron beam's current has multiple
advantages: reducing the strain on the polarized electron
source, proportionally lowering synchrotron radiation (the
main source of the detector's background); and, offering
the possibility of increasing the electron beam's energy:
Plans are to use a non-zero crossing angle at the Large
Hadron Collider (LHC) at CERN . In this case,
reducing the bunch's length would directly contribute to
increasing the luminosity and eliminating the necessity of
having a crab-crossing system .
Hence, high-energy hadron cooling may play important
role in increasing the performance of high-energy hadron
and lepton-hadron colliders, including RHIC and eRHIC
at Brookhaven National Laboratory, BNL, the Tevatron at
Fermilab, and the LHC at CERN.
Electron cooling proved to be very efficient method of
cooling intense hadron- and ion-beams at low and
medium energies . The electron cooler of 9 GeV
antiprotons in the Fermilab recycler represents state-of-
the-art technology . Development of the ERL-based
electron cooler at BNL promises effective cooling of gold
ions with energies of 100 GeV per nucleon .
Nevertheless, the effectiveness of electron cooling is
weaker for protons than it is for ions (it scales with Z2/A,
where Z is the change number of an ion and A its atomic
number, viz., Z2/A=1 for protons and Z2/A=31.7 for
1qAu'). It also falls sharply with the beam's energy (for
RHIC it falls as y712 , where y=E/mc2 is the relativistic
factor of a particle). Hence, traditional electron-cooling of
protons with energies from about 100 GeV (RHIC) to a
few TeV (LHC) with conventional techniques is hardly
possible within the realm of present accelerator
The idea of coherent electron cooling (CEC) [10,11]
encompasses various possibilities of using collective
instabilities in the electron beam to enhance the
effectiveness of the interaction between hadrons and
electrons. In this paper, we focus on a specific case of
using a high gain FEL (driven by an ERL) for CEC. CEC
combines the advantages of electrostatic interaction with
the broad band of FEL-amplifiers: examples in this paper
span from tens of THz to hundreds of PHz. Such systems
are naturally fit into a straight section of modern high-
energy hadron colliders. The proposed CEC method has
some potential advantages compared with the concept of
optical stochastic cooling :
a) it may not entail significant modifications to the
lattice of the hadron machine ;
b) it uses electrostatic interaction instead of very
inefficient radiation and interaction with TEM
waves by protons in a wiggler;
c) it is not limited to few potential choices of laser
frequencies and their bandwidths in THz range.
Similar to other coherent cooling techniques, the CEC's,
cooling rate is limited by the cross-talk of neighboring
hadrons (and the short noise in the electron beam). Thus,
the cooling rate is limited by an effective number of
particles in a coherent sample, which is inversely
proportional to the amplifier's bandwidth. In the CEC
scheme, the FEL frequency can be chosen appropriately
to match the energy of the electron beam. Consequently,
for LHC energies the FEL wavelength naturally extends
into the soft-X-ray range (nm), where frequencies are
measured in ExaHertzs (10"S Hz). Even a tiny fraction of
this frequency extends far beyond the bandwidth of any
Table 1. Comparison of estimations for various cooling mechanisms in RHIC and LHC colliders.
The sign o is used to indicate helplessly long damping times.
Machine Species Energy GeV/n Synchrotron radiation, hrs Electron cooling, hrs CEC, hrs
RHIC Au 100 20,961 - - 1 0.03
RHIC protons 250 40,246 o > 30 0.8
LHC protons 450 48,489 oQ > 1,600 0.95
LHC protons 7,000 13 (energy)/26 (transverse) 0000 <2
To estimate electron cooling in LHC we used an energy scaling y' typical for RHIC's electron cooler design [8,9], i.e., cooling
protons in LHC at 7 TeV is -10 harder that cooling antiprotons in the Fermilab recycler . Hence, our usage of mm in an
a p p r o p r i a t e c o 1 u m n
same straight section. It has a small, weak chicane at the
1. PRINCIPLES OF CEC AT HIGH end of the FEL section for adjusting the timing between
ENERGIES the electron-beam's modulation and that of the hadron.
This scheme imposes limitations on the value of the
Figure 1 shows two (of many) possible layouts of a wiggler parameter, a~, (see discussion in the following
longitudinal coherent electron cooler. As in a regular sections).
electron-cooling scheme, electrons and hadrons should A more elaborate scheme (which also is more flexible
have the same relativistic factor in the CEC: and complicated) separates the hadron- and electron-
E E beam so each can be individually manipulated.
Y =2(2) For simplification, let us initially consider longitudinal
MCC mhc (energy) cooling of the hadron beam. As shown in
The simplest (and most economical) version of the CEC Section 3, this cooling can be redistributed to include
allows electrons and hadrons to co-propagate along the transverse cooling. Otherwise, the principles of the FEL-
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LITVINENKO,V.N. FREE ELECTRON LASERS AND HIGH-ENERGY ELECTRON COOLING., article, August 31, 2007; United States. (https://digital.library.unt.edu/ark:/67531/metadc895398/m1/4/: accessed April 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.