FCChh DoubleSlot Beam Screen Density Profiles vs Slot

FCC-hh Double-Slot Beam Screen: Density Profiles vs Slot Size, Misalignments, and Magnet Temperature R. Kersevan, TE-VSC-VSM 26/11/2015

1. The whole rationale behind the double-slot design is the possibility of capturing a large fraction of the SR photons inside the annular space between the BS and the coaxial absorber (see C. Garion’s presentation at FCC Week in Washington for the one-slot version). The idea is to generate a large fraction of the molecules and photoelectrons as far away as possible from the area where the proton beam circulates, thus minimizing the beamgas scattering and the electron cloud issues 2. A recent internal review about the FCC-hh injection energy has requested a number of MC simulations showing the distribution of the SR photon as a function of the beam energy: the lower the latter, the broader (vertically) the SR fan, and correspondingly bigger is the number of molecules generated inside the BS 3. During a recent FCC-hh meeting the question of the sensitivity of the double -slot beam-screen (BS) concept to its vertical alignment inside the cold-bore (CB) of the magnets has been raised 4. In the following, the results of several coupled MC simulations for the SR photon distribution and the ensuing photo-desorption profiles are shown

Reminder: Double-Slot Beam-Screen Geometry

1 x 14. 3 m-long dipole followed by 1. 36 m-long drift section: wireframe model for ray-tracing analysis • • • 1 row of spacers/ribs Cusp-shaped absorber reflector (symmetric on opposite side of BS) • • View of the symmetric double-slot FCChh BS concept, slightly rotated. The coordinates of some relevant vertices are indicated (in cm) in the “vertex coordinates” pane. The length of the dipole has been assumed to be 14. 3 m (like LHC now). The dipole is straight, with the curved orbit adjusted so that the initial and final point of the orbit is in the center of the circular cold bore (CB ID= 22 mm). The sagitta of the orbit in the middle of the dipole is ~ 2. 4 mm. 4 x rows of spacers installed every 7. 5 cm from each other (in a direction parallel to the CB axis) are used to keep together the external part of the BS to the internal one and give structural strength during a quench event. They also absorb a large fraction of the photons entering the slot, after one or more reflections. On the external part the 2 x rows of spacers/ribs intercept, after reflection on the smooth curved cusp-shaped part, a large fraction of the impinging primary radiation, i. e. 221 W out of 502, or 44%.

Details of the geometry implemented for the drift section: tapered transitions • View of the exit area of the two drifts showing the different cross-sections: 1. Racetrack-shaped at the end of the dipoles (with local absorber in the crescent zone)… 2. … conical tapered zone going from racetrack to circular with larger ID… 3. … followed by taper/cylinder/taper to model the bellows/BPM parts (still to be designed in detail)… 4. … followed by final taper going from circular to racetrackshaped to connect to the following dipole (mirror geometry of the taper 1).

• • Close-by view of the drift area with tapers, highlighting the different power densities. In particular, it is evident a localized spike in power density on the taper-in part of the drift, immediately before the racetrack connection to the following dipole (in dark pink color). A total of few watts are absorbed at that location, out of the 502 W generated by a single dipole. This localized high-power density spot will generate a localized high outgassing rate and, possibly, if not mitigated, a source of high e-cloud photoelectron seeds (not discussed further here).

• • • Same as before, with color-coded SR power density textures. The highest power density is on the end-plate (crescent-moon) which closes the annular space between the internal and external part of the BS. Total power on 1 crescent is 42 W, or 8. 4% of the total power generated by one 14. 3 m-long dipole. The power density texture scale is logarithmic, that is why a non-zero photon density is shown even for the external part of the BS, and for the CB. The CB receives a very small fraction of the total power, 6. 3 m. W/dipole. This power is basically made up of lowenergy SR photons which leak out, after multiple reflections in the crescent space.

• • • Front view with ray-tracing of primary and scattered/reflected photons (@50 Te. V) Realistic scattering functions have been used, for copper with different levels of surface roughness R. R is 0. 004 (some units) for most of the surface of the BS, internally, but is decreased to 0. 001 (smoother, more reflecting) on the areas where most of the primary photons impinge. The spacer ribs have a higher roughness, even if they don’t need it because the impinging angle is very close to 90 deg. The footprint of the 4 non-continuous external pumping slots in the 4 crescent areas are visible, and highlighted by red circles. The position of the 4 pumping slots are asymmetric: further away from the plane of the orbit on the primary photons side (to decrease SR power leakage to the CB), and closer to the continuous slot on the opposite side, to reduce the conductance and improve the pumping efficiency (still to be optimized in position and size).

Case 1: Vertical size of the two slots increased from 3. 2 mm to 5: Effect of an increasing beam energy Note: the density bumps on the right of the figure are due to the assumption that the quadrupole/drift straight have NO beam-screen (and therefore NO cryogenic pumping. It is the relative value of the density along the dipole (flat part) which counts. Average densities shown on the right

Case 2: Nominal 3. 2 mm slots: Effect of a vertical offsets of 1 or 2 mm A misalignment of 2 mm increases the number of photons reflected towards the opposite side of the beam screen

Case 2: Nominal 3. 2 mm slots: Effect of a vertical offsets of 1 or 2 mm The average density more than doubles when the BS is vertically misaligned by 2 mm (Black Line: reference profile when photon scattering is not included)

Case 3: Nominal 3. 2 mm slots: density profile changes with CB temperature change The two red lines indicate areas along the CB where a suitable cryosorber would have to be placed in order to pump H 2 at 4. 5 K 1. The average density increases by > 4 x when the CB is not entirely pumping 2. Identifying the cryosorber and how to apply it inside the whole CB length is an open issue

Conclusions: • A vertical misalignment of the BS up to 2 mm generates a more than doubling of the gas density inside the BS • Vertically-enlarged slots along the BS produce a ~ 50% higher gas density inside of the BS (from 1. 04 E+15 to 1. 50 E+15 H 2/m 3) (also: to be checked effect on impedance/trapped modes) • A magnet design with a 4. 5 K CB implies a more than fourfold increase of the gas density, due to the fact that a cryosorbing material (possibly long and narrow strips, as modelled here) would need to take the place of the whole CB surface, which is the case for a 1. 9 K magnet, as the main pumping mechanism • The WP 4 Euro. Cir. Col collaboration program will address some of these issues (see companion presentation by C. Garion, at today’s meeting)