7 Design and Principles of Linear Accelerators and Colliders
313
holes and nose cones, and a schematic shape of a superconducting multi-cell cavity
(bottom). The corresponding electromagnetic field profile inside an elliptical cavity
is shown in Fig. 7.7b [1, 2].
The RF loss is proportional to the square of the surface current and proportional
to the resistivity. For a superconducting cavity, the microwave surface resistivity is
several orders of magnitude smaller than that of Cu, although it is not zero. The
shape of a superconducting cavity is optimised for properties such as: (1) reduced
excitation of higher order harmonics by the beam, (2) reduced surface magnetic field
to enhance the critical limit of the resultant superconducting to normal-conducting
phase transition, (3) reduced surface electric field to suppress field emission, and (4)
reduced multipacting behaviour [59–61]. The large iris opening and elliptical shape
result from these considerations.
Following Eq. (7.11), an RF power loss per meter of ~0.1 W/m is generated in
an accelerating cavity gradient of 1 MV/m, and it is proportionally increased with
.square of the frequency.
The above RF power loss dissipated into the 1.8 K cryogenic fluid needs to be
converted to an AC power load at room temperature using a total cryogenic efficiency estimate, η cr , which includes the ‘Carnot efficiency’ and the ‘thermodynamic
efficiency as follows:
η cr = η c η d = (P 1.8K /P 300K−i ) (P 300K−i /P 300K−r ) ,
(7.21)
where η c is the ‘Carnot efficiency’, η d is the ‘thermodynamic efficiency’ for the
compressor work at 300 K [2]. Assuming η c is ~1/(300/1.8) and η d is ~0.2 (typical
for large scale refrigerators), the total cryogenics efficiency η cr can be ~1/800.
Including this effect in the estimate of power loss, the relative RF power loss saving
factor of superconducting cavities, (surface resistance ~10 −5 lower than normalconducting cavities), may be approximately two orders of magnitude better in AC
power consumption performance for a CW operation. Therefore, superconducting
cavity technology enables the nearly entire (>99%) RF power to be transmitted to
the beam from the power source,
However, in case of the pulsed operation, which is the usual mode of normalconducting cavity operation, general power loss should be evaluated including a
duty factor, and is given by
(ωU/Q) × (pulse length) × (repetition rate) = (ωU/Q) × (duty factor) .
(7.22)
The pulse duration is typically in the μsec range in case of normal conducting
cavity operation, and the duty factor is normally about three orders of magnitude
smaller for normal-conducting cavity operation, compared with the superconducting
cavity operation. It results in the general power balance between the normalconducting cavity and superconducting cavity operation become in similar level,
with including the total cryogenic efficiency for the superconducting cavity operation. On the other hand, it should be noted that a pulse duration in the level of msec,
313
holes and nose cones, and a schematic shape of a superconducting multi-cell cavity
(bottom). The corresponding electromagnetic field profile inside an elliptical cavity
is shown in Fig. 7.7b [1, 2].
The RF loss is proportional to the square of the surface current and proportional
to the resistivity. For a superconducting cavity, the microwave surface resistivity is
several orders of magnitude smaller than that of Cu, although it is not zero. The
shape of a superconducting cavity is optimised for properties such as: (1) reduced
excitation of higher order harmonics by the beam, (2) reduced surface magnetic field
to enhance the critical limit of the resultant superconducting to normal-conducting
phase transition, (3) reduced surface electric field to suppress field emission, and (4)
reduced multipacting behaviour [59–61]. The large iris opening and elliptical shape
result from these considerations.
Following Eq. (7.11), an RF power loss per meter of ~0.1 W/m is generated in
an accelerating cavity gradient of 1 MV/m, and it is proportionally increased with
.square of the frequency.
The above RF power loss dissipated into the 1.8 K cryogenic fluid needs to be
converted to an AC power load at room temperature using a total cryogenic efficiency estimate, η cr , which includes the ‘Carnot efficiency’ and the ‘thermodynamic
efficiency as follows:
η cr = η c η d = (P 1.8K /P 300K−i ) (P 300K−i /P 300K−r ) ,
(7.21)
where η c is the ‘Carnot efficiency’, η d is the ‘thermodynamic efficiency’ for the
compressor work at 300 K [2]. Assuming η c is ~1/(300/1.8) and η d is ~0.2 (typical
for large scale refrigerators), the total cryogenics efficiency η cr can be ~1/800.
Including this effect in the estimate of power loss, the relative RF power loss saving
factor of superconducting cavities, (surface resistance ~10 −5 lower than normalconducting cavities), may be approximately two orders of magnitude better in AC
power consumption performance for a CW operation. Therefore, superconducting
cavity technology enables the nearly entire (>99%) RF power to be transmitted to
the beam from the power source,
However, in case of the pulsed operation, which is the usual mode of normalconducting cavity operation, general power loss should be evaluated including a
duty factor, and is given by
(ωU/Q) × (pulse length) × (repetition rate) = (ωU/Q) × (duty factor) .
(7.22)
The pulse duration is typically in the μsec range in case of normal conducting
cavity operation, and the duty factor is normally about three orders of magnitude
smaller for normal-conducting cavity operation, compared with the superconducting
cavity operation. It results in the general power balance between the normalconducting cavity and superconducting cavity operation become in similar level,
with including the total cryogenic efficiency for the superconducting cavity operation. On the other hand, it should be noted that a pulse duration in the level of msec,