Controlling Synchrotron Radiation Backgrounds in Detectors

Backgrounds I: Backgrounds I: Synchrotron Radiation Synchrotron Radiation Mike Sullivan USPAS 2022 MS_3 1

Outline Outline Backgrounds Detector backgrounds What are they? SR Beam-gas Luminosity SR Equation Simple calculations Important energy cuts Sources near the IR Beam tails Summary and conclusions 2

Beam backgrounds Beam backgrounds There are several sources of backgrounds from the stored beams that affect detectors Here we will go over some of the more prominent sources Synchrotron radiation This is just photons emitted by beam particles as they are accelerated (bent by the magnetic fields in the bending and focusing magnets) Beam-gas interactions This source is the collision between a beam particle and a gas molecule inside the beam pipe The collision itself generates some physics interactions that are considered backgrounds in the detector 3

Synchrotron radiation Synchrotron radiation This radiation is in the form of photons (mostly x-ray energies) in electron accelerators These photons generally cause background hits in the sub-detectors that are located very close to the beam pipe The total number of photons from this source can be quite daunting For example, the FCCee collider running at the Z0 (91.2 GeV Ecm) with beam currents of 1.4 A in 16640 bunches generates 1 1011 SR photons from the combination of the last (soft) bend magnet and the last 3 quadrupole magnets before the IR for each beam bunch. This comes out to 5 1018 photons/sec generated upstream of the collision point and headed for the IP The detector would prefer NOT to see more than maybe hundreds of photons from every collision we need to reduce the incoming photon rate by 9-10 orders of magnitude 4

SR sources (2) SR sources (2) The very high rate of photon generation means that this background must be the first to control Very small changes in the masking scheme or in the overall suppression plan can make a big difference in the expected hit rate in the detector This also means that secondary photon sources (i.e. reflection from surfaces or scattering from surfaces) can produce significant hits in the detector unless properly controlled One must also make sure that orbit deviations cannot produce SR photons that get around the masking design The overall rate can be high enough to produce photons that back-scatter from downstream surfaces, bounce back to the IP and increase the background hits in the detector Disclosure: I use cgs (cm, gram, sec) units most of the time but switch to meters (from cm) for most of the formulas coming up 5

When a charge accelerates it generates a transverse wave in the static Coulomb field that propagates at light speed. SR power equation SR power equation Charged particles radiate energy in the form of photons whenever they are accelerated The power radiated by a charged particle is a function of the acceleration squared This is the Larmor nonrelativistic formula The relativistic version of this equation is the Li nard formula Using the standard relativistic relations, we can calculate the energy loss for a particle in linear acceleration ?2 ?3 ? =2 2 ? 3 ?2 ??6 2 2 ? =2 ? ? ? 3 We use ? = ???2 and ? = ???to get the power for linear acceleration See Jackson 2nd edition, ch. 14 for more details 2 2 ?2 ?2 ?2 ?2??2 ??2 ? =2 ?? ?? =2 ?? ?? ? =2 1 ? ?? ?? 2 ? 1 ?? ?? ?2?3 ?2?3 ?2?3 3 3 ?? ?? 3 3 6

SR power SR power linear motion energy losses linear motion energy losses Looking at the last equation and using the following information ?2??2= 2.82 10 13cm and ??2= 0.511 MeV we have that the energy lost from radiation from linear acceleration for an electron is about 6 10 15 MeV for an acceleration of 1 MeV/m. The SLAC linac can produce up to about 20 MeV/m as can the superconducting linac at Jefferson Lab. Even the plasma accelerator in FACET at SLAC which has achieved nearly a factor of 1000 increase in accelerating gradient still has negligible energy loss from the acceleration. So, until we find a charged particle with a much smaller mass than the electron, linear accelerators will continue to have very low energy losses from radiation. The story is very different for circular machines. Even when we are not adding more energy to the charged particle by making it go faster, we lose energy because we are changing the direction of the momentum vector through the use of the magnetic fields of the bending and focusing elements (Lorentz force term v B term) 7

SR power SR power circular motion energy losses circular motion energy losses For charges going in a circle then the energy loss per turn is the following equation (again by Li nard) This is useful for calculating the total energy loss as the beam goes around the ring and how much RF power is needed to compensate for this energy loss This energy loss becomes very interesting for the detector folk when running at the ttbar energy The location of the RF becomes important because it changes the energy of the beam, and the detector wants to stay on the resonance ?2 ?2? ?2?4?4 where ? =2 ?2?3?2?2?2=2 3 3 ? = ?? ? with ? as the orbit radius For high-energy electrons ? 1 the energy loss per turn is then ?? ??? = 8.85 10 2?(???)4 ?(??????) The 4th power of the particle energy is the limiting factor. One can make bigger but only linearly. 8

Energy spectrum of SR Energy spectrum of SR There are many different plots of the energy spectrum of SR. Here is one of them. The important thing to know is the critical energy value This is the photon energy in which half of the total energy of the spectrum is below this value and half is above ? = ??????? In the table, notice that only 8.7% of the total number of photons in the fan are above the critical energy 9

Some handy formulas Some handy formulas For a horizontal bend there is an inherent vertical spread in the radiation which is usually very small for relativistic electrons. The approximate full width goes as 2/? where: ? = ? ???2 Critical energy 2 ? ??? 10 ?(???) = 6.65022 ?(??) To correctly calculate the vertical spread of the radiation fan one needs to include the angular spread of the beam in the vertical plane. This number is usually much larger than the inherent value above except in diffraction limited storage rings. This is important in estimating the power density of the radiation fan that strikes the surface of the beam pipe. 3 ? ??? 10 1 ? ??? = 2.21873 ? (??) 1 ? ??? = 2.21873 ?(??? )3 ? (?) For a proton 2.21873 3.583345 10 10 For a muon 2.509362 10 7 ????????? ? ??? ??= 3.2478 Some common relationships: One electron has charge of 1.602 10 19 Coulombs 1 A = 1 Coulomb/sec 1 W = 1 Joule/sec 1 eV = 1.602 10 19 Joules Formula for the number of SR photons knowing the total SR energy and the critical energy 10

Critical energy Critical energy The critical frequency is defined as: Derivation using the definition is given here The other handy formulas can be easily derived from this equation ?3 ?? 3 2 ????? ?3 ? ? ?????=3 2 ? = 1.9733 10 16 GeV-m ? ??2 with ??2= 5.11 10 4 GeV ? = Plugging in all the numbers on the right side we get 2.21873 x 10-6 GeV which translates to 2.21873 keV for the critical energy. 11

Magnet bending power A couple more A couple more handy formulas handy formulas is the bend radius and L is the magnet length is the total bend angle (radians) Here are some relationships to use when calculating SR power for a bend magnet The power/mrad comes in handy when one is estimating how many photons are striking a beam pipe surface that intercepts so many mrads of the fan Note the switch to cm for the magnet length in the 2nd formula for total power ? ? = 14085? ? ?4(???) ? ? ?2(?) = 0.127 ?2?? ?2??? ? ? ?(??) for a proton 14085 1.239 10 9 for a muon 2.229 10 5 ?(?) ???? = 14.085? ? ?4??? ? ? ? ?? ? ? ? 2)?? = 33.356 ? 2 tan( E= beam energy (GeV) B (kG-m) 12

Some rules of thumb Some rules of thumb Some K-shell energies keV Al 1.56 Fe 7.11 Cu 8.98 Ag 25.5 W 67.9 Au 80.7 SR photons with energies below 1 keV never contribute to detector backgrounds In fact, a minimum energy of 5 keV is usually a very reasonable cut Only a very thin wall Be beam pipe wall can pass any photons below this cut One thing to keep in mind is the K-shell energies of the materials that make up the beam pipe If a significant number of SR photons are above the K-shell energy many of these photons will be absorbed by the atoms and re-emitted isotropically at the K-shell energy giving them a better chance of penetrating the beam pipe From the table we see that a thin layer of Au (few m) on the inside of the central beam pipe can block a very high percentage of incident x-rays especially if the SR critical energy is low (10-30 keV) (see next slide) 13

Plots of the fraction of incident photons that scatter back out of a material as a function of the incident photon energy. What we see here is that at and above the k-shell energy of the element (9 keV for Cu and 81 keV for Au) the photon scatter rate increases by more than a factor of 10. The element is therefore very good as an absorber of x-ray energies below the k-shell energy. 14

More rules of thumb More rules of thumb About 3% of the incident photons on a beam pipe surface will scatter out of the wall There is some preference for the photons to forward scatter as opposed to backscatter. The difference is usually on the order of 2-3 (forward/backward). An estimate of the solid angle fraction of 2 that a central beampipe has with respect to an upstream beam pipe wall that scatters photons to the central chamber can be made using the following formula The central beampipe can be approximated as a disk of radius r1 and the source of photons can be located at z1 from the IP. The far end of the pipe is usually a small hole compared to the near end, but this can also be calculated and subtracted. Then the solid angle fraction of 2 for the beam pipe is just 1 estimate the number of photons hitting the inside wall of the central chamber. If this number is close to becoming significant then a more careful calculation/simulation needs to done. This approximation should be well within a factor of 10 of a more careful calculation. ?12 ?1 2. One can then 2 over 4 For a disk on axis the exact equation is: 1 ??? ???? ?1?1 15

Bending radiation from magnetic fields Bending radiation from magnetic fields We mentioned earlier that bending radiation dominates all electron machine designs linear accelerating radiation is very small The energy loss per turn feeds into the damping time of the beam This loss must be made up by accelerating the beam with RF cavities It also produces the natural emittance value The quantum effect of photon emission generates a spread in the beam We now concentrate on the SR that matters for the IR Here we will look at the possible sources and for us the bending field can come from dipoles or quadrupoles 16

IR sources of SR IR sources of SR The last bending magnet before the IP always sends SR through the collision point The fan of radiation from the bending magnet goes right up to the beam axis Most designs make the last bending magnet as soft as possible so that the SR fan has mostly low-energy photons Any quadrupoles between the last bend magnet and the IP are also sources of SR These magnets (when correctly positioned) make a cone or cylinder of SR generated by the beam particles that are not going straight down the quad axis Any particle with a small offset from the axis experiences a bend field given by the gradient x offset Most of the beam particles are very close to the quad axis and hence generate very soft photons that travel with the beam and do not have much angular divergence However, beam particles that are many beam sigmas out in either X or Y can produce higher energy photons (from the higher bend field) that also diverge at large enough angles to be a possible source of detector background 17

PEP PEP- -II Interaction II Interaction Region SR fans from Region SR fans from bending magnets bending magnets The PEP-II IR design is symmetric for the incoming and outgoing beams. It also has the extra bending from the B1 dipole magnets. There are fans of bending radiation on the incoming beams from the design offset orbits in the Q2 (LER) and Q4 (HER) magnets. PEP-II Interaction Region LER bend fans of SR HER bend fans of SR 18

The KEKB IR was designed so that all incoming quads were on axis thereby minimizing incoming SR. The inner most quads were shared by both beams, so the outgoing beams go though these quads with a significant offset thereby generating bending fans of SR. KEKB Interaction Region SR KEKB Interaction Region SR fans from bending magnets fans from bending magnets 19

Summary Summary Controlling the bend radiation around an IR is the first step in controlling the detector background In high current machines, the SR levels can be orders of magnitude over acceptable background levels Knowing the critical energy of a synchrotron radiation fan, one can use several techniques to determine the importance of this fan of radiation with respect to possible detector background levels 20