i) to obtain a slanting irradiated surface (i.e. make θi as small as possible) to reduce the ... The number of gas molecules emitted by one photon is the PSD rate.
High-Intensity Synchrotron Radiation Effects Y. Suetsugu High Energy Accelerator Research Organization, Tsukuba, Japan Abstract Various effects of intense synchrotron radiation on the performance of particle accelerators, especially for storage rings, are discussed. Following a brief introduction to synchrotron radiation, the basic concepts of heat load, gas load, electron emission, and the countermeasures against these effects are discussed. Keywords Accelerator vacuum system; synchrotron radiation; photon stimulated gas desorption; photoelectron; heat load.
1
Introduction
Recent high-power (that is, high-current and high-energy) particle accelerators generate intense synchrotron radiation (SR). This is a good photon source. However, it has the following potentially harmful effects on accelerator performance: i)
heat load: damage to beam pipes or instruments,
ii) gas load: short lifetime, noise to particle detectors, iii) electron emission: beam instabilities, gas load, iv) radiation: radiation damage. The first three effects are directly related to the beam and the vacuum system. In this paper, basic and practical concepts to understand the three effects are presented, along with measures to treat these problems, that is, to protect the machine in a broad sense. These problems affect accelerator vacuum systems, but they have widespread effects upon overall machine performances as well. The understanding of these problems is also useful in designing and constructing accelerators.
2
Synchrotron radiation
Synchrotron radiation comprises electromagnetic waves emitted when a high-energy charged particle is accelerated in a direction orthogonal to its velocity, such as in a magnetic field (Fig. 1) [1]. The SR is useful as a photon source. The main features of SR compared to other photon sources are: –
high intensity and high photon flux,
–
wide range of wavelengths, from infrared to hard X-ray,
–
well understood spectrum intensity,
–
high brightness,
–
high polarization ratio.
Fig. 1: Synchrotron radiation
An accelerated charged particle emits electromagnetic radiation. The radiation fields (electric field E and magnetic field B ) are given by using electromagnetic potentials:
∂ E = − A − ∇φ , B = ∇ × A . ∂t
(1)
Here, ϕ and A are the Lienard-Wiechert scalar and vector potentials, which are given by
A(t ) =
e e β 1 = , ϕ (t ) , 4πε 0 c R (1 − n ⋅ β ) ret 4πε 0 R (1 − n ⋅ β ) ret
(2)
where R (tret ) is the distance vector from the source to the observer (see Fig. 2), and tret is the retarded
time, ctret= ct − R (tret ) , and β is the ratio of the velocity v to the speed of light c (that is,
β = v / c ). Hence the electric and magnetic fields are obtained by 1 n × E = B ret , c E =
2 n−β e 1− β 4πε 0 R 2 1 − n ⋅ β 3
(
(
)(
)
(3)
e n× n − β ×β + . 4πε 0 c R 1 − n ⋅ β 3 ret ret
)
( (
)
)
(4)
At observing points far from the emitting point, the radiation field of the latter term of E (∝ 1/R) is more important, and the former term can be neglected.
Fig. 2: Coordinate system
The pointing vector, that is, the radiation energy flow toward R per unit area, is given by
S r (t= )
1 E×B =
µ0
1
µ0 c
E 2 1 − β ⋅ n n = ε 0 cE 2 1 − β ⋅ n n
(
)
(
ret
)
Then, the instantaneous differential radiation per unit solid angle dΩ becomes
dP 2 e2 = n ⋅ SR = ε 0 cE 2 1 − n ⋅ β R 2 = ret ret dΩ 16π 2ε 0 c
(
.
(5)
ret
)
n×
{(
}
n −β ×β 5 1− n ⋅ β
(
)
2
.
)
(6)
ret
If β is parallel to β ,
dP e 2 β 2 sin θ 2 = dΩ 16π 2 ε 0 c (1 − β cos θ )5 On the other hand, if β is orthogonal to β ,
(
.
)
2 dP e 2 β 2 (1 − β cos θ ) − 1 − β 2 sin θ 2 . = dΩ 16π 2ε 0 c (1 − β cos θ )5
(7)
(8)
For both cases, when β ≈ 1, the term (1 − β cosθ ) approaches zero if θ approaches to zero (see Fig. 3). This means that the power beams to the front of the orbit. This is called ‘beaming’. The angle of beaming θ is given by 5
= θ
1
γ
, γ =
Ee Ee [MeV] 1 (for electron) . = = 2 0.511 1 − β 2 m0 c
(9)
Electric line of force
β
