6 Design and Principles of Synchrotrons and Circular Colliders
287
In general, the external circuit which is often in vacuum and at cryo-temperature
includes a low-noise amplifier to couple the induced current signal to room
temperature, and thus enable plasma diagnostics. The input noise temperature of
the amplifier is, depending on its coupling to the resonant circuit, closely related to
the minimum achievable temperature of the particles in the trap. Most frequently, the
impedance Z (with the real part R) shown in Fig. 6.42 is implemented as inductance
L so that the circuit becomes resonant at the oscillation frequency of the ions. This
is to tune out (compensate at resonance) the parasitic capacitance of the electrodes.
This inductance may be implemented as discrete solenoid coil made of copper or
superconducting wire. The quality factor Q = R/ωL of the tuned circuit has to be
large to guarantee efficient resistive cooling A high Q in turn means to incorporate a
low loss network. As a caveat it should be mentioned that extremely high Q values
(above say 10 5 ) may be problematic if the bandwidth of the resonance becomes
smaller than the width of the particle spectrum. For further reading we refer to [197],
where Shockley presents the basic equations for trapped and charged particles in a
Penning trap.
There exist a large number of other cooling techniques used in traps, such as
collisional cooling, RF- and optical sideband cooling (resolved and unresolved
sideband methods) and sympathetic cooling. The list of examples given here is
certainly not exhaustive and a detailed description can be found in review articles
[189]. As for the term RF cooling (which may be confounded with RF-sideband
cooling) [189] it should be pointed out that this refers to a reduction of temperature
or vibration amplitude of a microscopic cantilevered bar in vacuum using an RF
resonant circuit which is fed externally with a few milli-Watt of RF power [198].
Acknowledgements The authors would like to thank Michael Blaskiewicz, Paul Derwent,
Christina Dimopoulou, Wolfgang Hofle, Fritz Nolden, Rolf Stassen and Junxia Wu for their
contribution to this chapter and Jens Vigen for reading and correcting the manuscript.
References
1. E. Wilson, B.J. Holzer: Beam Optics, this handbook, Chapter 2.
2. B.J. Holzer: Lattice Design in High Energy Accelerators, Proc. CERN Accelerator School,
CERN-2006-002.
3. LHC Design Report, CERN-2004-003.
4. W. Herr, B. Holzer, B. Muratori: Concept of Luminosity, this handbook, Sect. 6.4.
5. K. Steffen: Periodic dispersion suppressors II, DESY-HERA 83/02, 1983.
6. R. Brinkmann: Insertions, Proc. CERN Accelerator School, CERN-1987-010.
7. Proceedings of CERN Accelerator School: Beam Injection, Extraction and Transfer, 2017,
Erice, CERN-2018-008-SP, 2018
8. V. Mertens. Kicker and septa technology, Chapter 5.5.
9. Y. Yamazaki ed., “Accelerator Technical Design Report for J-PARC”, KEK Report 2002-13;
JAERI-Tech 2003-044, 2003.
10. J. Wei et al., Evolution of the Spallation Neutron Source Ring Lattice, Proc 20 th ICFA
Advanced beam dynamics workshop, Chicago IL, 2002,
287
In general, the external circuit which is often in vacuum and at cryo-temperature
includes a low-noise amplifier to couple the induced current signal to room
temperature, and thus enable plasma diagnostics. The input noise temperature of
the amplifier is, depending on its coupling to the resonant circuit, closely related to
the minimum achievable temperature of the particles in the trap. Most frequently, the
impedance Z (with the real part R) shown in Fig. 6.42 is implemented as inductance
L so that the circuit becomes resonant at the oscillation frequency of the ions. This
is to tune out (compensate at resonance) the parasitic capacitance of the electrodes.
This inductance may be implemented as discrete solenoid coil made of copper or
superconducting wire. The quality factor Q = R/ωL of the tuned circuit has to be
large to guarantee efficient resistive cooling A high Q in turn means to incorporate a
low loss network. As a caveat it should be mentioned that extremely high Q values
(above say 10 5 ) may be problematic if the bandwidth of the resonance becomes
smaller than the width of the particle spectrum. For further reading we refer to [197],
where Shockley presents the basic equations for trapped and charged particles in a
Penning trap.
There exist a large number of other cooling techniques used in traps, such as
collisional cooling, RF- and optical sideband cooling (resolved and unresolved
sideband methods) and sympathetic cooling. The list of examples given here is
certainly not exhaustive and a detailed description can be found in review articles
[189]. As for the term RF cooling (which may be confounded with RF-sideband
cooling) [189] it should be pointed out that this refers to a reduction of temperature
or vibration amplitude of a microscopic cantilevered bar in vacuum using an RF
resonant circuit which is fed externally with a few milli-Watt of RF power [198].
Acknowledgements The authors would like to thank Michael Blaskiewicz, Paul Derwent,
Christina Dimopoulou, Wolfgang Hofle, Fritz Nolden, Rolf Stassen and Junxia Wu for their
contribution to this chapter and Jens Vigen for reading and correcting the manuscript.
References
1. E. Wilson, B.J. Holzer: Beam Optics, this handbook, Chapter 2.
2. B.J. Holzer: Lattice Design in High Energy Accelerators, Proc. CERN Accelerator School,
CERN-2006-002.
3. LHC Design Report, CERN-2004-003.
4. W. Herr, B. Holzer, B. Muratori: Concept of Luminosity, this handbook, Sect. 6.4.
5. K. Steffen: Periodic dispersion suppressors II, DESY-HERA 83/02, 1983.
6. R. Brinkmann: Insertions, Proc. CERN Accelerator School, CERN-1987-010.
7. Proceedings of CERN Accelerator School: Beam Injection, Extraction and Transfer, 2017,
Erice, CERN-2018-008-SP, 2018
8. V. Mertens. Kicker and septa technology, Chapter 5.5.
9. Y. Yamazaki ed., “Accelerator Technical Design Report for J-PARC”, KEK Report 2002-13;
JAERI-Tech 2003-044, 2003.
10. J. Wei et al., Evolution of the Spallation Neutron Source Ring Lattice, Proc 20 th ICFA
Advanced beam dynamics workshop, Chicago IL, 2002,