# Radiation issues In the Fermilab Booster Magnets\*

E. Prebys^\#^, Fermilab, Batavia, IL 60510, U.S.A.

Abstract

The demands of the Fermilab neutrino program will require the lab's 30+
year old 8 GeV Booster to deliver higher intensities than it ever has.
Total proton throughput is limited by radiation damage and activation
due to beam loss in the Booster tunnel. Of particular concern is the
epoxy resin that acts as the insulation in the 96 combined function
lattice magnets. This paper describes a simulation study to determine
the integrated radiation dose to this epoxy and a discussion of the
potential effects.

## Introduction

The Fermilab Booster is described in detail elsewhere \[1\]. It is a
rapid cycling synchrotron, which accelerates a proton beam from 400 MeV
to 8 GeV at an instantaneous rate of 15 Hz. The lattice consists of 96
combined function magnets arranged with 2 horizontally focusing and 2
horizontally defocusing in each of 24 identical periods. The cross
sections of the two types of magnet are shown in Figure 1. The entire
magnet body is in vacuum in order to eliminate the need for a beam pipe.

![](media/image1.png){width="2.220138888888889in"
height="1.6840277777777777in"}![](media/image2.png){width="2.20625in"
height="1.6340277777777779in"}

The field is produced by 56 coils of water cooled copper conductor. The
coils are potted in an epoxy resin which acts as an insulator. Because
the magnet is inside the vacuum volume and there has not been a magnet
failure in over 30 years, it has not been possible to inspect this
insulation for radiation damage directly.

## Booster LOSS Simulation

### Interaction Model

This study uses the MARS Monte Carlo program \[2\] to simulate the
interaction of the beam protons with the magnets. A simple model of the
magnet has been created which includes the magnetic yoke, the current
carrying coils, and the insulating epoxy. An approximate model of the
magnetic field is also included as it could affect the shower
development. The incident beam is evenly distributed in a swath 4 cm
wide and 1 mm high along the top edge of the magnet to simulate a
reasonable range of beam motion.

### Incident Beam Rate

It is very difficult to accurately determine the amount of beam
deposited in the individual magnets of the Booster. We will make an
estimate based on the observed beam loss. Figure 2 shows a typical 33 ms
Booster acceleration cycle. The overall efficiency is between 80 and
85%, with the majority of the beam lost shortly after injection. A
significant amount of this lost beam ends up in the Booster collimator
system, so for the sake of this model we will assume beam loss of 10% at
1% at discrete energies of 500 MeV and 5 GeV respectively.

Recently, the Booster has been delivering an average of about
$5 \times \text{10}^{\text{16}}$ protons/hr
($1\text{.}4 \times \text{10}^{\text{13}}$ protons/sec) outside of major
down times \[3\]. If we naively assume that the lost beam is evenly
distributed over the magnets, this leads to the following rates for
incident beam on each magnet

-   500 MeV: $1\text{.}4 \times \text{10}^{\text{10}}$ p/sec

-   5 GeV: $1\text{.}4 \times \text{10}^{9}$ p/sec

![](media/image3.jpeg){width="2.3625in" height="1.8423611111111111in"}

In fact, the lost beam is divided between the top and bottom faces, but
as we will see, beam loss on either face leads to similar integrated
dose on the top and bottom coils, so for the sake of simplicity, we
deposit the entire beam loss in the top face in the simulation.

## Results![](media/image4.png){width="2.5340277777777778in" height="2.5416666666666665in"}![](media/image5.png){width="2.4923611111111112in" height="2.497916666666667in"}

### Instantaneous Energy Deposition

Figure 3 shows the longitudinal profile of the energy deposition at both
energies. Based on this, the first 50 cm are taken as the shower maximum
and used to determine the peak of the energy deposition in the
insulator. Figure 4 shows then rate of energy deposition in this region.
We see that both energies result in peak energy losses of about
$1\text{.} \times \text{10}^{- 3}$ Gy/sec in the volume of the epoxy
resin.

As a cross check of our assumptions, Figure 5 shows the MARS calculation
of the residual radiation at the front face after 30 days of operation
and 1 day of cool down. This is consistent with surveys done in the
Booster.

### Total Dose

Recalling the total proton rate that we started with, the instantaneous
energy deposition above corresponds to an energy deposition on the order
of $1 - 2 \times \text{10}^{- \text{17}}$ Gy per accelerated proton. The
Booster has accelerated about $1 \times \text{10}^{\text{21}}$ protons
in its years of operation \[5\], so this corresponds to roughly 10-20
kGy of total dose. Recalling that Booster was significantly less
efficient for most of its life and the fact that beam loss is different
in different periods, it is reasonable to assume that some areas of
insulation may have received as much as 100-200 kGy.

![](media/image6.png){width="2.8305555555555557in"
height="2.761111111111111in"}![](media/image7.png){width="2.6555555555555554in"
height="2.5791666666666666in"}

### Projected Dose

The Booster is expected to deliver on the order of
$5 - \text{10} \times \text{10}^{\text{21}}$ protons over the next 10
years \[6\]. The ability to deliver these protons will necessarily
involve decreasing beam loss, but it is still reasonable to project that
this will result in exposures of up to 1 MGy in some areas of the magnet
insulation.

![](media/image8.png){width="2.9472222222222224in"
height="2.870138888888889in"}![](media/image9.png){width="2.873611111111111in"
height="2.808333333333333in"}

## DISCUSSION

Unfortunately, there is little information on the details of the epoxy
used in the Booster magnets. In typical epoxy resins of this type,
detectable radiation damage begins to occur with exposure at the few
hundred kGy level \[7,8\], but the first symptoms are embrittlement and
an increase in moisture absorption. The former should not be a worry
unless it becomes extreme. The latter might be a concern in that
moisture could affect the conductivity of the resin; however, as the
coils are in vacuum, this is not an issue. Epoxy resins in the magnets
at the Tristan ring at KEK had exposure as high as 10 MGy and while they
were visibly darkened they continued to function properly \[9\].

## Conclusions

Our studies indicate that the epoxy resin used as an insulator in the
magnets of the Fermilab Booster may have received integrated radiation
doses as high as 100 kGy over the life of the machine. The increased
proton flux needed by the neutrino program could mean that some areas
will receive as much as 1 MGy over the next ten years.

While these numbers are within the range where epoxy resins have been
shown to work in the past, they are definitely at a level which causes
some concern, particularly given our lack of details about the exact
epoxy used. It is therefore extremely important to keep beam loss at a
minimum in the coming years and to try to keep it as uniform as possible
to avoid excessive localized dosage.

Further study is warranted, and should a magnet fail for other reasons,
it will be important to inspect the condition of the epoxy.

## References

\[1\] E. L. Hubbard, *et al*, "Booster Synchrotron", FERMILAB-TM-405
(1973).

\[2\] http://www-ap.fnal.gov/MARS/

\[3\] E. Prebys, "Status of the Proton Plan", *talk presented at URA
site review*, Fermilab BEAMS-DOC-1817 (2005).

\[4\] N.V. Mokhov, A.I. Drozhdin, P.H. Kasper, J.R. Lackey, E.J. Prebys,
R.C. Webber, "Fermilab Booster Beam Collimation and Shielding",
*presented at PAC03*, FERMILAB-CONF-03-087 (2003).

\[5\] Dave Finley, private communication.

\[6\] E. Prebys, B. Baller, W.J. Spalding, "The Proton Plan",
FERMILAB-BEAMS-DOC-1441 (2004).

\[7\] Lin Fu, R.A. Fouracre, H.M. Banford, "An Investigation of
Radiation Damage in a Cured Epoxy Resin System Using Regression
Experiment Design", *presented at conference on Electrical Insulation
and Dielectric Phenomena,* CEIDP.1988.26320 (1988).

\[8\] R.A. Fouracre, A. Al-Attabi, H.M. Banford, "Effects of Radiation
Doses up to 2 MGy on the Thermally Stimulated Discharge Current Spectra
for a Cured Epoxy Resin System", *presented at conference on Electrical
Insulation and Dielectric Phenomena,* CEIDP.1992.283250 (1992).

\[9\] K. Endo, K. Egawa, Y. Ohsawa, T. Michikawa, "Estimation of
Radiation Dose to Epoxy Resin by IR Spectrophotometry", *presentation at
EPAC 96*, KEK-PREPRINT-96-55 (1996).