Copper coating specification for the RHIC arcs Page: 2 of 8
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Copper coating specification for the RHIC arcs
BNL, Upton NY 11972, USA
Copper coating specifications for the RHIC arcs are given. Various upgrade scenarios are consid-
ered and calculations of resistive wall losses in the arcs are used to constrain the necessary quality
and surface thickness of a copper coating . We find that 10 pm of high purity copper will suffice.
I. INTRODUCTION AND THEORY
Typical parameters for an eRHIC  are shown in Table I. W\e will be concerned with ohmic losses on the pipe
walls. For a round beam pipe the power loss per meter is given by 
P'=MQ2 dR(oe-" 2/2
4ir2bTc ] R(j ~2c
where R, (w) is the surface resistivity as a function of angular frequency. For room temperature and low frequencies
R, = Zowp/2c, where Zo = poc = 377g. Room temperature resistivities give ohmic losses of 0.5 W/m for a
stainless steel beam pipe and 0.12 W/m for a copper one. The previously used upper limit for losses in the arcs is
0.5 W/m . Cooling the stainless steel pipe to 4K will reduce it's resistivity but magneto-resistance will increase
it. It therefore seems prudent to reduce the ohmic losses by coating the beam pipe with copper. A device for in-
situ coating is described in  and previous calculations have assumed that one can count on a factor of RRR=100
reduction in resistivity leading to a coating thickness of 5 m. There are two problems with this procedure. Firstly,
magneto-resistance at 3.45T and an RRR of 100 doubles the effective resistivity of the copper . Secondly, even with
an effective RRR=50, the mean free path of an electron in the copper is l = 2 m, which is the skin depth at 20 MHz.
This was estimated using the formula [3} 1 = (po e)/p where polo = 6.6 x 10tS4nm2 for copper. When the mean free
path is longer than the skin depth the current at one location in the metal will be influenced by signficantly different
electric fields at other locations and one needs to include convection in the electron transport . This calculation
was done in  for a ray of light with normal incidence. For wavenumber k = w/c the electric field satisfies
-3iZok Idlr r_- r
TABLE I: RHIC ring parameters
circumference C = 3834m
revolution period and frequency T = 12.8 s = 1/fo
maximum charge per bunch (2 = 32 nC
minimum rms bunch length t-8 = 5 cm
bunches in the ring M = 180
room temperature copper resistivity pc = 1.7 x 10a S2m 
RRR for copper 100
room temperature stainless resistivity ps = 3.6 x 10- Qm
beam pipe radius b = 3.6 cm
*Electronic address: blaskiewicztbn1.gov
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Blaskiewicz, M. Copper coating specification for the RHIC arcs, report, December 1, 2010; United States. (digital.library.unt.edu/ark:/67531/metadc846206/m1/2/: accessed February 18, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.