in the VLHC Tunnel A Very Large Lepton Collider Eberhard Keil keil/doc/vllc/09mar01.pdf CERN, Geneva, Switzerland
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1 A Very Large Lepton Collider in the VLHC Tunnel Eberhard Keil CERN, Geneva, Switzerland keil/doc/vllc/09mar01.pdf E. Keil page 1
2 Programme VLLC parameter searches with a notebook and packages in Mathematica vllc.nb is specific to VLLC, p, Packages contain formulae valid for many machines and e e vllc.nb finds parameters of VLLC arcs in thin-element approximation, synchrotron radiation, RF system, collective effects, etc. vllc.nb writes short file with parameters for MAD MAD finds solutions for finite elements, corrects chromaticity, tracks, etc. Verify VLLC parameters of Sen and Norem Would I design a VLLC in the same manner? E. Keil page 2
3 Mathematica Input Data colle, inje Collision, injection energy in Volt, R Bending, average radius of arc cells in Meter circ Circumference in Meter phaseadv Phase advance in arc cells/2 supern Number of superperiods IPx, Beam-beam tune shift parameter IPy Amplitude functions at IP in Meter bunchk Number of bunches/beam totl Design luminosity in Meter Second frf Approximate frequency of RF system in 1/Second tauq Quantum lifetime in Hour Note Mathematica dimensions A few parameters for wigglers and collective effects missing E. Keil page 3
4 Collider Parameter Table from Mathematica *colle Volt Meter *R Meter *circ Meter totarcl Meter revolf /Second *bunchk 89 bunchs Meter dipoleb Second Volt/Meter Asterisks ( ) mark input parameters E. Keil page 4
5 #"! $" IP Parameter Table from Mathematica 0.1 IPy 1., 0.05 Meter IPx, bunchn bunchi Ampere Meter Meter Meter Meter Meter "! lumic /Second Meter lumib beami Ampere /Second Meter checkl E. Keil page 5
6 % ' Arc Parameter Table from Mathematica *phaseadv 0.25 periodn periodl Meter perioda Meter Meter & x Meter Av. Av. max maxdx Meter focall Meter quadl Meter E. Keil page 6
7 " Wiggler Parameter Table from Mathematica *epsf 1.01 plusl Meter sigef lossf polf taup Hour Meter Meter )( Av. Max. quadg Second Volt Meter E. Keil page 7
8 + $ #! Synchrotron Radiation Table from Mathematica Volt *! lossu Ampere Volt * powersr powersrm Ampere Volt/Meter Second, crite Joule/Coulomb 1/(Meter Second) * totphotons distsr Meter incidencea spotsr Meter powsrm Ampere Volt/Meter E. Keil page 8
9 + RF System Table from Mathematica hrf lambdarf Meter frf /Second bucketh overv Volt! *! voltrf / % Meter. buncharea Second Volt *tauq 24 Hour E. Keil page 9
10 MAD Data File!-- Define arc parameters mu2pi:=0.25 arcr:=30444 rho:=25411 circ:= periodn:=856 periodl:= dipolel:= focall:= quadl:= frees:= return E. Keil page 10
11 Cell Definition in MAD qfa: quad l=quadl k1=1/focall/quadl qda: quad l=quadl k1=-1/focall/quadl la: drift l=frees/2; lsa: drift l=frees/6 sextl:=frees/6 sfa: sext l=sextl k2=+0.1; sda: sext l=sextl k2=-0.1 set v1 1/4/sin(pi*mu2pi)ˆ2; set v2 (1-1/4/sin(pi*mu2pi)ˆ2) ba: rbend l=dipolel, & angle=(2*pi)/(4*supern*(v1+v2)+2*(periodn-2*supern)) cold: rcollimator xsize=xcolda ysize=ycolda colf: rcollimator xsize=xcolfa ysize=ycolfa ca: line=(lsa,sfa,lsa,ba,la,cold,qda,cold, & lsa,sda,lsa,ba,la,colf,qfa,colf) Note that cell definition is practically number-free E. Keil page 11
12 Arc Cell Parameters VLLC for IIT study - 9 to 11 March 2001 Unix version 8.51/04 26/02/ β 1/ 2 (m 1/ 2 ) Dx (m) β y 1 / 2 β x 1 / 2 D x s (m) δ E/ p 0c = 0. Table name = TWISS 0.50 E. Keil page 12
13 7 8 6 Horizontal Dispersion without Synchrotron Radiation VLLC for IIT study - 9 to 11 March 2001 Unix version 8.51/04 26/02/ D x Dx (m) s (m) δ E/ p 0c = 0. Table name = TWISS [*10**( 3)] E. Keil page 13
14 6 Horizontal Dispersion with Synchrotron Radiation 1.2 VLLC for IIT study - 9 to 11 March 2001 Unix version 8.51/04 26/02/ Dx (m) s (m) δ E/ p 0c = 0. Table name = TWISS [*10**( 3)] E. Keil page 14
15 9 6 Horizontal Orbit Offset due to Synchrotron Radiation VLLC for IIT study - 9 to 11 March 2001 Unix version 8.51/04 26/02/ x x (m) s (m) δ E/ p 0c = 0. Table name = TWISS [*10**( 3)] E. Keil page 15
16 < : = turns ; no SR up to Horizontal Tracking Results: 10 e VLLC for IIT study - 9 to 11 March 2001 Unix version 8.51/04 02/03/ p0 [ *10**( - 3)] px/ x (m) Table name = TRACK E. Keil page 16
17 < : = turns > no SR up to Vertical Tracking Results: 10 e VLLC for IIT study - 9 to 11 March 2001 Unix version 8.51/04 02/03/ p0 [ *10**( - 3)] py/ y (m) Table name = TRACK [*10**( -3)] E. Keil page 17
18 :? no SR turns up to Long. Tracking Results: 10 e VLLC for IIT study - 9 to 11 March 2001 Unix version 8.51/04 01/03/ pt ct (m) Table name = TRACK E. Keil page 18
19 SR turns Horizontal Tracking Results: 300 e ID Entries ID Entries E E-05 Mean RMS E E-02 Mean RMS PX x X rad /mm Mathematica MAD envelope E. Keil page 19
20 : " SR turns Longitudinal Tracking Results: 300 e ID Entries ID Entries E E-02 Mean RMS E E-02 Mean RMS DELTAP B( /mm A Mathematica MAD envelope E. Keil page 20
21 C C D, " LKJ I Wiggler Magnets arrangement C C Homogeneous-field dipoles in T in same direction as in arc dipoles wigglers field plusb In poles Compute total length plusl of Polarization requires field in wigglers a factor ratiob smaller in arc dipoles Wigglers effective in VLLC with low, decrease damping times. and bunchlength E( Always increase energy spread Wigglers may be photon cutters & Damping wigglers installed at, e.g. in collision below nominal current F reduce equilibrium emittance m achieve E( H G( Used at injection with plusl & Emittance wigglers installed at F increase equilibrium emittance, ratio is called hwbyhb best in dispersion bumps with used in VLLC below maximum energy E. Keil page 21
22 VLLC Operation at 45 GeV with Wiggler Magnets *lowepsf 100 *lowhwbyhb 4 lowplusl Meter lowtaup Hour )(M Meter M Max.!! bunchnc Meter L Meter L beamic Ampere Second Meter " totlc E. Keil page 22
23 R Z Y Z Y H H Collective Effects: Transverse Mode Coupling Instability S, voltage, e Q. Bunch current threshold with synchrotron frequency transverse and transverse loss factors NPO VXW. S Y Q. N O. V[W H mm V/pC at V\W. Scale RF cavities by number from LEP with ma at 20 GeV with my Find ma at 184 GeV, and arrangement of damping wigglers at injection N]O! N]O V/pC at! V\W Scale shielded bellows from LEP with 10 m spacing and mm. ma at 20 GeV with my Find ma at 184 GeV, and arrangement of damping wigglers at injection N O N]O TMCI dominated by bellows and below design current by factor 10 E. Keil page 23
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