Simulating synchrotron radiation in accelerators including diffuse and specular reflections

An accurate calculation of the synchrotron radiation flux within the vacuum chamber of an accelerator is needed for a number of applications. These include simulations of electron cloud effects and the design of radiation masking systems. To properly simulate the synchrotron radiation, it is important to include the scattering of the radiation at the vacuum chamber walls. To this end, a program called synrad3d has been developed which simulates the production and propagation of synchrotron radiation using a collection of photons. Photons generated by a charged particle beam are tracked from birth until they strike the vacuum chamber wall where the photon is either absorbed or scattered. Both specular and diffuse scattering is simulated. If a photon is scattered, it is further tracked through multiple encounters with the wall until it is finally absorbed. This paper describes the synrad3d program, with a focus on the details of its scattering model, and presents some examples of the program’s use.

Figure 1

Smooth surface photon reflectivity $R$ for a 10 nm C film on Al substrate [15].

Figure 2

The vacuum chamber is the union of a number of subchambers. This figure illustrates this showing two subchambers—one colored green and the other colored red.

Figure 3

A subchamber is defined by a number of cross-sectional slices. (A) A subchamber (red) and two cross-sectional slices (blue). (B) A given cross section is defined by a number of vertices.

Figure 4

Specular reflection probability [13], vs. photon energy and angle, for an rms surface roughness of $\sigma =200\mathrm{nm}$. The curves have been calculated from Eq. (1) with $R=1$.

Figure 5

Diffuse scattering polar angular distributions for 30 eV photons, $\sigma =200\mathrm{nm}$ and $T=5500\mathrm{nm}$. The full diffuse scattering expression [Eq. (a97)] has been used to calculate these curves.

Figure 6

Diffuse scattering out-of-plane angular distributions for 30 eV photons, $\sigma =200\mathrm{nm}$ and $T=5500\mathrm{nm}$. The full diffuse scattering expression [Eq. (a97)] has been used to calculate these curves.

Figure 7

Diffuse scattering polar angular distributions for high energy photons, $\sigma =200\mathrm{nm}$ and $T=5500\mathrm{nm}$. The curves are calculated from the approximate relation given in Eq. (3). In this case, high-energy photons correspond to $\lambda \ll \sigma$, i.e., $E\gg 6\mathrm{eV}$.

Figure 8

Diffuse scattering out-of-plane angular distributions for high energy photons, $\sigma =200\mathrm{nm}$ and $T=5500\mathrm{nm}$. The curves are calculated from the approximate relation given in Eq. (3). In this case, high-energy photons correspond to $\lambda \ll \sigma$, i.e., $E\gg 6\mathrm{eV}$.

Figure 9

Comparison of data [18] and model for diffuse scattering at 5° from a rough ($\sigma =200\mathrm{nm}$) surface layer on an aluminum substrate.

Figure 10

Comparison of data [18] and model for diffuse scattering at 45° from a rough ($\sigma =200\mathrm{nm}$) surface layer on an aluminum substrate.

Figure 11

Comparison of data [18] and model for diffuse scattering at 85° from a rough ($\sigma =200\mathrm{nm}$) surface layer on an aluminum substrate.

Figure 12

Photon trajectories from a dipole in three dimensions. The photon source is on the right. For purposes of illustration, the transverse geometry has been distorted from an ellipse to a circle, and the longitudinal dimension has been shrunk by a factor of 10. Black lines are trajectories, and blue dots are photon absorption sites. Photons generated by the beam propagate downstream (to the left in the figure) and strike the vacuum chamber. Some are absorbed, but most scatter and strike the vacuum chamber further downstream. The absorption site locations tend to be clumped in several clusters (at the location of downstream dipoles), with decreasing intensity as we get further from the source.

Figure 13

CesrTA beam pipe cross-section. The vacuum chamber (middle) is 9 cm wide and 5 cm high. The cooling water chamber (left) and pump chamber (right) were not part of the simulation.

Figure 14

Absorbed photon distribution vs. polar angle averaged over each type of magnetic environment. Zero angle corresponds to the radial outside direction. The different colors correspond different scattering conditions: (a) Black: pure specular scattering; (b) Cyan: scattering from a polished surface with $\sigma =4\mathrm{nm}$, $T=200\mathrm{nm}$; (c) Blue: scattering from a rough surface with $\sigma =100\mathrm{nm}$, $T=5500\mathrm{nm}$; (d) Red: scattering from a rough surface with $\sigma =200\mathrm{nm}$, $T=5500\mathrm{nm}$.

Figure 15

ILC damping ring schematic layout.

Figure 16

Vacuum chamber designs for magnetic elements in the ILC damping ring. The upper part of the figures correspond to the outer radius of the ring, when installed.

Figure 17

Photon absorption distributions in different magnetic environments (QUADRUPOLE, WIGGLER, DRIFT and SBEND) and ring regions (Arc1, Arc2, and Wiggler) for the ILC damping ring.

Figure 18

Coordinate system illustrating the vectors ${\mathbf{k}}_{\mathbf{1}}$ and ${\mathbf{k}}_{\mathbf{2}}$.

Figure 19

Coordinate system illustrating the vectors $\mathbf{r}$, ${\mathbf{r}}_{\mathbf{0}}$, and $\mathbf{n}$.