Quadrupole Radiation and Beam Tails in Accelerators

Bkgds Bkgds II: Quadrupole II: Quadrupole radiation and Beam tails radiation and Beam tails Mike Sullivan USPAS 2022 MS_4 1

Quadrupole radiation Quadrupole radiation The diagrams to the right illustrate how quadrupoles generate SR The incoming beam is either parallel (see diagram) or is slightly expanding The first magnet encountered by the beam is the horizontal focusing magnet hence in the vertical plane the beam is defocused (1st diagram) Because the second magnet is vertically focusing the horizontal part of the beam must be over- focused in the 1st magnet so that the defocusing of the 2nd magnet is compensated for But as can be seen, this produces SR photons in the horizontal plane that are difficult to shield against that come from the defocusing bend (or reverse bend) in the 2nd magnet (the vertical magnet) 2

SR masking procedure SR masking procedure First, block all incoming SR from upstream bending magnets and prevent direct hits from SR on the central beam pipe The central beam pipe is usually the thin Be beam pipe at the center of the detector Include in this effort all bend SR photons that might scatter from the upstream beam pipe surface and one bounce to the central chamber This should also include SR photons that pass through the central region and strike beam pipe surfaces that are downstream and backscatter to the central beam pipe Second, look at quadrupole SR and see if at least most of this radiation can be blocked so that direct hits are not possible This is not necessarily completely possible (see the previous slide) If successful or as good as can be, then you check the beam pipe surfaces where the quad SR does hit and determine if the one bounce rate to the central beam pipe from these surfaces is possibly too high 3

Beam particle distribution Beam particle distribution We now come to the next important topic which is the transverse beam distribution After shielding the central beam pipe from any bend radiation fans, we then concentrate on the quadrupole radiation As we saw in the previous slide, beam particles with large offsets in the final focus magnets (especially beam particles at high x) can make SR photons that can have a chance of directly hitting the central beam pipe This is also the reason that central beam pipes cannot be super small The smaller the radius of the central chamber the more likely photons from beam particles at lower sigma values can directly strike the beam pipe One usually has to install a synchrotron mask with an even smaller radius than the central beam pipe This mask can make a local impedance bump that might upset the beam 4

Beam transverse distribution (2) Beam transverse distribution (2) The core transverse beam distribution is a gaussian with independent sigmas for each plane (x/y) The beam size (beam sigma) at any location is calculated by knowing the emittance and the beta function at that Z location The IP final focus quads usually contain the highest beta function values of the entire ring (sometimes 10-100 times higher than anywhere else) Some examples of the maximum beta values of various machines and designs X (m) Y(m) PEP-II HER 500 450 PEP-II LER 90 165 KEKB HER 360 585 KEKB LER 250 280 FCCee Z 2000 10000 FCCee Top 1000 5400 5

Beam tails or beam halos Beam tails or beam halos Beam tails are beam particles that populate out at higher beam sigmas where they increase the particle density to higher values than one would expect from a gaussian distribution The beam transverse profile becomes wider than the expected gaussian profile These beam tail particles are the result of perturbations encountered around the storage ring Any perturbation can put beam particles out in these higher sigma orbits. A partial list is here. The collision with the other beam produces primarily a vertical tail Scattering from gas molecules in the ring Internal bunch scattering (i.e. Touschek scattering) Bunch to bunch coupling through wake fields left behind in the beampipe Anything that can perturb a beam particle can push some of these particles into the tail region 6

Beam tails (2) Beam tails (2) Electron rings have the capability of generating a fairly large beam tail distribution that can be more or less stable This is because electrons have a very strong damping factor in the emission of SR around the ring This strong damping term is constantly working to bring the beam tail particles back into the core gaussian distribution We have a constant flow outward from the perturbations and a constant flow inward from the SR damping term 7

Beam tails and collimators Beam tails and collimators Accelerator folk are not overly concerned about beam tails as long as the tail is a small percentage of the core and as long as the tail distribution does not affect the stored lifetime If the ring dynamic aperture is large, then the beam lifetime will remain high even with a large tail distribution Collimator settings will then determine the beam lifetime However, the detector is much more sensitive to these beam tails and the backgrounds (especially the increased SR photons) from these beam tails can severely increase the detector background levels Why is the detector so sensitive? One of the main reasons is that the beam is largest in the final focus elements. Therefore, the number of acceptable beam sigmas is limited by the size of the beam pipe in these elements. Beam particles at sigma values larger than the beam pipe will crash into the pipe here and spray background particles into the detector. Hence, the ring collimators are used to cut into the beam tails and thereby reduce the detector background 8

Beam tail distributions Beam tail distributions Because the non-gaussian beam tails are generated by a large number of possible sources it is difficult to calculate an overall tail distribution The source terms also vary with time some are more important when the vacuum pressure is high while others can become important if the bunch charge is large A beam tail distribution coming from a particular source can be calculated but it is difficult to get all of the source terms correct at the same time I use a second, wider gaussian beam tail distribution to model a real tail distribution A second gaussian distribution is a reasonable approximation as the tail distribution is semi-stable The second gaussian has two unknowns The width which is given by a factor times the core sigma The height as compared to the core gaussian This is done separately in both dimensions (X and Y) I ask that the horizontal height and the vertical height of the tails be the same reducing our 4 unknowns to 3 This model can then be used to calculate SR backgrounds, and the entire beam transverse distribution is the sum of these four gaussians 9

Beam transverse distribution plots Beam transverse distribution plots Tail distributions that can generate the background level seen in the superKEKB pixel detector (PXD). 1 2 2 1 core They also approximately agree with the measured beam lifetime. See next slide for more detailed information. 3 core 3 This comparison was in 2019. 10

The 3 beam tail distributions in the previous slide generated PXD background levels that came close to matching the measured background. Information about the beam tails Information about the beam tails Formula used to generate the core + beam tail distributions Estimated beam lifetimes 2?2 2?? ?2? ????= ??? ?2 ?2 2?? 2+ ???? ??2?2 2 ?? 2 The dotted lines are beam particle values where the beam lifetime is as shown if a collimator is located at the beam sigma where the beam profile crosses the dotted line. 2 2?? 2?? Table of beam tail parameters for the cases shown on the previous slide For instance, the case 2 profile in the X plane crosses the 10 min. line at a x of about 14.5. Therefore, the beam lifetime for the case 2 profile in X is 10 min. if a collimator is located at 14.5 x. Beam Tail Ax Bx Ay By % core 1 0.04 0.33 0.04 0.17 2.7 2 0.025 0.30 0.025 0.17 1.2 3 0.03 0.35 0.03 0.20 1.3 This is derived from a calculation by M. Sands that concludes that collimating a core beam distribution at 6 reduces the beam lifetime to 1 day. I set the beam tail total integral to be not much more than 5% of the core. Too large a tail will distort core measurements (i.e. luminosity, beam sizes, etc. 11

Beam Beam- -stay stay- -clear clear All storage rings have a beam-stay-clear definition This is the distance from the center of the beam to any material part of the beam pipe The vacuum chamber must be outside of this number It is usually defined in terms of beam sigmas plus some extra for orbit distortion The PEP-II B-factory definition in the IR was: 15 x + 2mm where x is the uncoupled x (that is, all of the emittance is in the X plane) 15 y + 2mm where y is the fully coupled y (half of the total emittance is in the Y plane). The 15 fully coupled sigmas translated to about 65 standard sigmas. The values changed to 12 + 5mm beyond 30 m from the IP The beam pipe in the final focus magnets came right down to this beam envelope 12

BSC (2) BSC (2) The BSC defines how big an aperture is needed in the final focus magnets This sets how big the final focus magnets have to be in order to meet the strength requirements The size of the FF magnets pushes on the available detector acceptance and sets a minimum angle for particle detection from the collision For this reason and because the detector solenoidal magnetic field usually encompasses the final focus magnets the FF magnets are super-conducting The large beam size in the FF magnets (usually the largest in the ring), the need to push right down to the BSC with the vacuum chamber so the FF magnets can be built and the fact that nearly all of the rest of the vacuum chamber in the ring is far away from the BSC means that the IP is the natural bottleneck for beam particles that are escaping from the stored beam This is where the collimators in the ring come into play 13

Beam tails summary Beam tails summary Non-gaussian beam tail distributions are sometimes overlooked in electron storage rings These non-gaussian effects are also important in light sources The non-gaussian tail can become a significant factor especially in the early running of a storage ring It usually determines the beam lifetime until some of the early generating sources (like beam-gas interactions) decrease with more running time as the ring vacuum improves. (More on this coming up) Either lost beam particles or SR from beam tails generally tend to dominate the detector backgrounds until a few years (or at least several months) of running have occurred 14