1. Minimizing the RF fields
on the superconducting surface of an SRF cavity
by optimizing its shape
REU 2009
Valery D Shemelin,
LEPP, Cornell University
for
David Stark,
University Minnesota Twin Cities
Valery Shemelin Accelerating Cell: Shape and Fields

2. Superconducting accelerating cavity: what are they for?
A key component of the modern particle accelerator is the device that imparts energy to the charged particles.
Single cell and multicell elliptical cavities.
Radio frequency (RF) cavities are used to accelerate charged particles to high speeds. The electric field inside the cavity kicks a charged particle passing through it. A large speed is attained after the particle travels through many cavities. A typical cavity generates a potential of over 1 million volts. If we tried to do the same thing using ordinary 9 volt batteries, for example, we would need more than 100,000 batteries.
A conventional copper cavity requires a lot of power to produce a high potential. The power being dissipated in the cavity walls can be as high as 1 million watts. As a result, copper cavities cannot operate continuously at high potential; superconducting radio frequency (SRF) cavities must be used for this purpose. The power dissipation in an SRF cavity is about 100,000 times smaller than in a copper cavity. Special materials and extremely cold temperatures are needed to make a cavity superconducting. An SRF cavity made of niobium is operated at a temperature of about -456 °F or 2 Kelvin (K).
Valery Shemelin Accelerating Cell: Shape and Fields

3. What accelerating cavities does the world want today?
ILC wants high gradient (31.5 MV/m is the base line of the project, but 40, 50 MV/m – who will mind?)
ERL wants moderate gradients (20) but low losses (refrigerator)
What are the issues for each application?
How do we design the cell to make these issues less problems?
Valery Shemelin Accelerating Cell: Shape and Fields

4. Comparison of some cells…
Valery Shemelin Accelerating Cell: Shape and Fields

5. Fields in a reentrant cavity TESLA and Reentrant cavity
Fields in the cavity
Epk/Eacc and Hpk/Eacc define maximal fields on the surface of the cavity. They are responsible for X-radiation: Epk, and thermal breakdown (quench): Hpk.
Fields in a reentrant cavity
TESLA and Reentrant cavity
Electric and Magnetic field:
Valery Shemelin Accelerating Cell: Shape and Fields

6. …their electric field along the profile line
The best shape (just aesthetically) should have a more regular dependences for these curves
Valery Shemelin Accelerating Cell: Shape and Fields

7. …and magnetic field on the profile line
Valery Shemelin Accelerating Cell: Shape and Fields

8. Case of the reentrant cavity: elliptic and a 6-arc curve
The reentrant cell with 20 % higher electric field and 10 % lower magnetic field than in TESLA cell, shape and electric field along the profile line.
We can divide the iris ellipse into two parts (or more but it will be too complicated) and deal with them separately.
However, I could not make a flat H-field profile…
Valery Shemelin Accelerating Cell: Shape and Fields

9. Attempt to flatten the H field
Upper part of this shape consists of straight segments
This ugly shape gives the best result for
δe ≤ 20 %
Valery Shemelin Accelerating Cell: Shape and Fields

10. Valery Shemelin Accelerating Cell: Shape and Fields
THE TASK
Find the shape having Epk/Eacc = 2.4
(+20 % to TESLA, TESLA has 2.0),
and minimum Hpk/Eacc.
We had the world record with Hpk/Eacc = 37.8 Oe/(MV/m),
-10 % relative to TESLA.
I hope that we can have -15 %. Even -12 % would be a good result.
This is a computational work. The work is supposed to be done with a SuperLANS 2D computer code, designated for designing of axially symmetric RF devices, their fields, losses and other Figures of Merit.
Valery Shemelin Accelerating Cell: Shape and Fields