ANSWERS TO NICOLAAS KOS FOR HIS PAPER Cold Beam Vacuum System for the LHC IR Upgrade Phase-1

Transcription

1 ANSWERS TO NICOLAAS KOS FOR HIS PAPER Cold Beam Vacuum System for the LHC IR Upgrade Phase-1 Maximum acceptable width for the pumping slots for a new beam screen wall thickness of 1.5 mm (SS only, and then on top of it a Cu layer of mm as now)? Heat load on the beam screen from image currents? Impedance requirements for the cold to warm transitions at both ends? Elias Métral, 20/01/2010 1/24

2 OBSELETE BEAM SCREEN DESIGN In particular for the supports Cooling tube Support Pumping holes Beam screen (in SS with a Cu layer) Copper layer Cold bore Elias Métral, 20/01/2010 2/24

3 LHC design as it is built and installed CURRENT BEAM SCREEN (1/14) In dipoles, also called baffles, to avoid direct e - path along magnetic field lines to the cold bore (which would then add to the heat load) Saw teeth in the arcs on Cu (a series of 30-μm high steps spaced by 500 μm in the long. direction, to reduce the forward reflectivity) Weld Elias Métral, 20/01/2010 3/24

4 CURRENT BEAM SCREEN (2/14) Elias Métral, 20/01/2010 4/24

5 CURRENT BEAM SCREEN low B? In the past, I used 1.8E-10 Ωm at low B and 5.5E-10 Ωm at high B (due to magnetoresitance effect) Bunch charge (for nominal) Q = e = 18.4 nc Rms bunch length σ z = 7.5 cm Bunch spacing S b = 7.5 m Cold bore inner radius d = 2.5 cm Covered surface from the holes In the arcs: f = 4.0% In the LSS: f = from 1.8% to 2.6% (depends on screen Φ) Elias Métral, 20/01/2010 5/24

6 CURRENT BEAM SCREEN (4/14) The power loss goes with the square of the bunch charge => It is ~ 2 times more for the ultimate bunch (1.7E11 p/b) compared to the nominal one (1.15E11 p/b) Power loss Theoretical computation with a previous design Meas. of LHC dipole beam screen samples without magnetic field + extrapolation Elias Métral, 20/01/2010 6/24

7 CURRENT BEAM SCREEN (5/14) Results shown by A. Mostacci (La Sapienza, University of Rome) during Francesco Ruggiero Memorial Symposium (CERN, 3 October 2007) for the power loss due to the pumping holes: access?contribid=54&sessionid=14&resid=1&materialid=slides&confid=20082 Elias Métral, 20/01/2010 7/24

8 CURRENT BEAM SCREEN (6/14) Using A. Mostacci s Mathematica Notebook (wwwslap.cern.ch/collective/ mostacci/slots/note/slots.nb), and updating the numerical values (only small changes), these curves were produced (constant power in mw/m vs. the beam screen thickness T and the width of the slots W) b arcs = 36.8 / 2 = 18.4 mm Elias Métral, 20/01/2010 8/24

9 CURRENT BEAM SCREEN (7/14) b LSS = 37.6 / 2 = 18.8 mm and f = 2.6 % (most critical case) Elias Métral, 20/01/2010 9/24

10 CURRENT BEAM SCREEN (8/14) The current parameters of the beam screen are Length of the slots: L = 6,7,8,9 and 10 mm => Laverage = 8 mm Width of the slots: In the arcs: W = 1.5 mm In the LSS: W = 1.0 mm Beam screen thickness: In the arcs: T = 1 mm SS mm Cu = mm In the LSS: T = 0.6 mm SS mm Cu = mm => Power loss from the holes in the arcs: P arcs 1.1 mw/m Power loss from the holes in the LSS: P LSS 0.1 mw/m In the most critical case Elias Métral, 20/01/ /24

11 CURRENT BEAM SCREEN (9/14) Power loss from the image currents in the beam screen (neglecting the holes) at 7 TeV, assuming a Gaussian bunch and the classical formula for the longitudinal resistive-wall impedance (with beam pipe radius b) => It was checked by N. Mounet that the same numerical result is obtained with our more precise multi-layer impedance formula G,RW P,1layer loss/ m = 1 2 π R Γ 3 4 M b N b e 2 π 2 c ρ Z 0 2 σ t 3 / 2 85 mw/m Γ 3 = Euler gamma function M = number of bunches = 2808 ρ 20K Cu = Ωm LHC circumference = 2 π R = m b = beam screen half height = 36.8 / 2 = 18.4 mm N b = p/b σ t = 0.25 ns Elias Métral, 20/01/ /24

12 CURRENT BEAM SCREEN (10/14) Concerning the power loss from the image currents due to the weld Long discussions in the past on the impact of the welding => Whether or not the image current would avoid the high impedance welding. The conclusion was that the image current DOES NOT avoid the high impedance region (except at VERY low frequencies), and thus for the losses the straight forward way of calculation can be used (see before: it assumes a constant H Φ on the wall, i.e. it is the first order solution) Elias Métral, 20/01/ /24

13 ρ 20K Cu = Ωm CURRENT BEAM SCREEN (11/14) A. Mostacci found in his thesis ( /files/thesis pdf), page 108, that the factor ¼ of the previous slide should be ~ 0.9 (in the initial geometry used in the previous slide, square, the weld was in the corner, i.e. protected from the bunch field, which explains the smaller factor) => I will use a factor 1 (conservative approach) below N. Kos confirmed that we have only 1 weld now of width 2 mm (i.e. over 2 mm there is no Cu but SS) Δ l Weld 2 π b = 2 2 π 18.4 = 1 π ρ 20K SS = Weld Ωm => P loss/ m Weld P loss/ m G,RW,1layer 57 % P loss/ m 48 mw/m Even though the weld corresponds to only ~ 1/60 of the surface, the power loss due to the weld is not negligible Elias Métral, 20/01/ /24

14 CURRENT BEAM SCREEN (12/14) Anomalous skin effect: Attributes the anomalous increase of surface resistance of metals at high frequencies and low temperatures to the long mean free path of the conduction e - => When the skin depth becomes much smaller than the mean free path, the classical theory breaks down => Increases slightly the power loss (see next slide) For the theoretical part, see Anomalous Skin Effect and Resistive Wall Heating, W. Chou and F. Ruggiero, LHC Project Note 2 (SL/AP): cdsweb.cern.ch/record/691905/files/project-note-2.pdf For the measurement part, see Surface Resistance Measurements of LHC Dipole Beam Screen Samples, F. Caspers et al., EPAC2000: accelconf.web.cern.ch/accelconf/e00/papers/mop7b11.pdf Reminder: The numerical value used for the Cu resistivity already takes into account the magneto-resistance effect Elias Métral, 20/01/ /24

15 CURRENT BEAM SCREEN (13/14) Comparison with A. Mostacci s results in his thesis ( cdsweb.cern.ch/record/516355/files/thesis pdf), Table 3.7, page 111 He considered b = bx = 22 mm and I considered b = by = 18.4 mm Elias Métral, 20/01/ /24

16 CURRENT BEAM SCREEN (14/14) Comparison between what I re- estimated and what is in the LHC Design Report, Vol. 1, Chap. 5 ( Vol_1_Chapter_5.pdf) => For 1 single beam ~ 85 mw/m (with the same formula as F. Ruggiero in his paper CERN SL/95-09 (AP)). Mostacci found ~ 80 mw/m (with simulations). The value quoted comes from meas. ~ 1 mw/m for the most critical pumping holes in the arc beam screen (very close to Mostacci s result) ~ 48 mw/m. Mostacci found 27 mw/m Elias Métral, 20/01/ /24

17 UPGRADED TRIPLET BEAM SCREEN (1/7) As part of the LHC IR Upgrade Phase-1, the existing Q1, Q2, Q3 and D1 magnets in the Atlas (IR1) and CMS (IR5) interaction regions will be replaced D1 beam vacuum will change from a room temperature system to a cold system Elias Métral, 20/01/ /24

18 UPGRADED TRIPLET BEAM SCREEN (2/7) Elias Métral, 20/01/ /24

19 UPGRADED TRIPLET BEAM SCREEN (3/7) Cold bore inner radius (provisional estimate) d = 55.3 mm Elias Métral, 20/01/ /24

20 UPGRADED TRIPLET BEAM SCREEN (4/7) Concerning the power loss from the pumping slots Covered surface from the holes f = 5.1 % b = 94.5 / 2 = mm For W = 1.5 mm (and T = mm) the power loss is ~ 0.1 mw/m If we allow ~ 10 mw/m (per beam), one can increase W to ~ 2.5 mm Elias Métral, 20/01/ /24

21 UPGRADED TRIPLET BEAM SCREEN (5/7) Concerning the power loss from the image currents in the beam screen (neglecting the holes) G,RW P,1layer loss/ m 1 b => If b goes from 36.8 / 2 = 18.4 mm to 94.5 / 2 = mm, then the power loss should decrease by a factor / 18.4 ~ 2.6 Elias Métral, 20/01/ /24

22 UPGRADED TRIPLET BEAM SCREEN (6/7) Concerning the power loss from the image currents from the weld Weld P loss/ m Δ l G,RW,1layer b P loss/ m Weld Width of the weld => P Weld loss/ m Δ l Weld b 2 => If one considers a width of the weld of 3 mm (instead of 2 mm at present), and if b goes from 36.8 / 2 = 18.4 mm to 94.5 / 2 = mm, then the power loss should decrease by a factor (2/3) (47.25 / 18.4) 2 ~ 4.4 Elias Métral, 20/01/ /24

23 UPGRADED TRIPLET BEAM SCREEN (7/7) IN SUMMARY, for 1 beam at nominal intensity => Comparison between the proposed upgraded triplet beam screen (what I computed in blue) and the present arc beam screen (table from the Design Report and what I recomputed in maroon) ~ 85 mw/m ~ 33 mw/m ~ 1 mw/m ~ 3.5 mw/m for T = mm and W = 2.2 mm ~ 48 mw/m ~ 11 mw/m FOR THE 2 BEAMS AT ULTIMATE INTENSITY => The above results should be multiplied by 4: factor 2 to go from 1 beam to 2 beams, and factor 2 to go from nominal to ultimate intensity Elias Métral, 20/01/ /24

24 GENERAL RULE FOR THE TRANSITIONS Try to use a maximum tapering angle of ~ 15 deg (the smaller the better!) Elias Métral, 20/01/ /24