Measurements and modeling of stray magnetic fields and the simulation of their impact on the Compact Linear Collider at 380 GeV

The Compact Linear Collider (CLIC) targets a nanometer beam size at the collision point. Realizing this beam size requires the generation and transport of ultralow emittance beams. Dynamic imperfections can deflect the colliding beams, leading to a collision with a relative offset. They can also degrade the emittance of each beam. Both of these effects can significantly impact the luminosity of CLIC. In this paper, we examine a newly considered dynamic imperfection: stray magnetic fields. Measurements of stray magnetic fields in the Large Hadron Collider tunnel are presented and used to develop a statistical model that can be used to realistically generate stray magnetic fields in simulations. The model is used in integrated simulations of CLIC at 380 GeV including mitigation systems for stray magnetic fields to evaluate their impact on luminosity.

Figure 1

Full measurement setup for survey stray fields.

Figure 2

Placement of the sensors relative to the beam pipe.

Figure 3

Schematic diagram of the elements in LSS5. Relative lengths are to scale.

Figure 4

PSD of the magnetic field (right-hand side scale) in the $x$, $y$ and $z$-direction, $P_{B,x}(f,s)$, $P_{B,y}(f,s)$ and $P_{B,z}(f,s)$ respectively, and total PSD $P_B(f,s)$ vs location $s$ (left-hand side scale) and frequency $f$.

Figure 5

Standard deviation of the magnetic field ${\sigma }_B(s)$ in the $x$ direction (blue), $y$ direction (orange), $z$ direction (green) and total (red) vs location $s$.

Figure 6

Correlation of the magnetic field with respect to $s=30\mathrm{m}$ (right-hand side scale) in the $x$, $y$ and $z$-direction, $C_{B,x}(f,s)$, $C_{C,y}(f,s)$ and $C_{B,z}(f,s)$ respectively, vs location $s$ (left-hand side scale) and frequency $f$.

Figure 7

(a) Stray field PSD $\overline{P_{B,\mathrm{ref}}}(f)$ vs frequency $f$ and (b) standard deviation $\overline{{\sigma }_{B,\mathrm{ref}}}(f)$ vs frequency $f$.

Figure 8

A sample from the generator of stray fields. (a) PSD $P_B(f,s)$ (RH scale) vs location $s$ (LH scale) and frequency $f$ and (b) correlation $C_B(f,s)$ (RH scale) vs location $s$ (LH scale) and frequency $f$. The correlation was calculated with respect to the stray field at $s=30\mathrm{m}$.

Figure 9

Transfer function of the beam-based feedback system $T(f)$ vs frequency $f$.

Figure 10

Transfer function of a mu-metal cylinder with 1 mm thickness and inner radius of 1 cm $T(f)$ vs frequency $f$.

Figure 11

(a) Effective stray field PSD $P_{B,\mathrm{eff}}(f)$ vs frequency $f$ and (b) standard deviation ${\sigma }_{B,\mathrm{eff}}(f)$ vs frequency $f$: without mitigation (blue); including a beam-based feedback system (orange); including a 1 mm mu-metal shield (green); and with the feedback system and mu-metal shield combined (red).