BEAM PHYSICS NOTES

Beam Physics Notes are informal notes meant to encourage and document the free scientific debate in accelerator research; they are circulated under the sole responsibility of the author, without any interference nor responsibility from the management. They can be telegraphic-style, even possibly hand-written or consist of photocopies, for example of slides presented at a Beam Physics Discussion, but should contain a front page (for which both LaTeX and Word templates are available) with a short abstract and a progressive registration number. An archive of these notes is kept by the SL-AP secretariat, while each new note is announced by e-mail to the mailing list beam-physics-notes@listbox.cern.ch. To register a new Beam Physics Note or to get a copy of a previous one, please contact Juliette.Thomashausen@cern.ch


List of Beam Physics Notes

NUMBER
DATE
TITLE
AUTHOR
ABSTRACT
60
08/08/2001 Considerations about Pb ions at injection plateau of the SPS L.Vos I compute the space charge tune shift and give estimations of intra beam scattering behaviour of lead ion bunches intended for collisions in the LHC at the injection plateau of the SPS for several scenarios.
59
28/06/2001 Symplectic matrix Algebra J. M. Jowett This note documents a Mathematica package for working with symplectic matrices. The illustrative examples include the use of the symplectic unit matrices, the symplectic conjugate and the manipulation of exact and approximate matrices including the symbolic representation of a combined-function bending magnet. A function to symplectify matrices is provided. Like the other functions in the packages it works on matrices of any even dimension to arbitrary precision (examples are given for 16 digits, 99 digits and infinite precision).
58
.06/07/2001 Tracking to verify the IR3 design for Version 6.2 D. Kaltchev This report outlines a simple procedure, based on off-momentum tracking of ~10^3 halo particle per dp/p value, sufficiently accurate to verify the IR3 ideal design parameters (also enumerated here). The lattice section used begins at the primary collimator in IR3 and extends for one turn around the ring. We use the error-free thick element optics for Beam 1, Version 6.2. The procedure will be further extended to study halo propagation with collimator misalignment and optical errors.
57
23/05/2001 Self-Consistent LHC bunch orbits for asymmetric injection schemes H. Grote The nominal LHC injection scheme assumes symmetry in the bunch population of ring-1 and ring-2 with respect to IP1 and IP5, where the first bunch of ring-1 collides with the first bunch of ring-2, and so on. Here we study the effect on the self-consistent closed orbits when this symmetry point is moved either to IP2 (and IP6), or to the centre of an arc.
56
03/04/2001 SODD: A Physics Guide F. Schmidt The Program SODD (Second Order Detuning and Distortion function) calculates the detuning distortion and Hamiltonian terms for arbitrary complex accelerators structures up to second order in the four-dimentional phase space. Starting from the linear lattice functions and the strength of the multipoles these terms are determined in first order of the multipole strength and in second order of all possible pairs of multipoles. This report documents the formulae of the various terms as coded in the program.
55
06/03/2001 Focusing at low energy  A. Verdier The merits of FODO and FO cells are compared. It appears that cylindrical magnetics lenses could be attractive for the first circulator of the neutrino factory thanks to their better optics performance, simpler design.and possible integration in the RF cavities. Some more studies are needed to assess the actual potentialities of cylindrical lenses and to launch a possible optimisation.
54
09/02/2001 What is the operational scenario required for the spectrometer magnets in IP2 and IP8  W. Herr Following a discussion with P. Proudlock and a request in a recent meeting of the Performance and Layout Committee (31.01.01) I should like to present the constraints for the operation of spectrometers in IP2 and IP8 during the injection process.
53
18 Jan 01 Run Environment for SixTrack F. Schmidt This note will describe how massive tracking campaigns can be performed with SixTrack starting from a MAD input file of the LHC lattice. The idea is to launch these runs as automatic as possible with minimal knowledge of either UNIX scripts or SixTrack input. 
52
18 Dec 00 The Syndrome of the Closed Orbit Correction in the LHC Arcs  S. Fartoukh This paper presents analytical results concerning the closed orbit corrector system of the LHC arcs.
51
18 Dec 00 Damping Wiggler Section for CLIC  F. Zimmermann Considering a damping ring where radiation damping, quantum excitation and intrabeam scattering only occur in a few long wiggler sections - the rest of the ring being transparent -, I show that by a proper choice of wiggler strength, wiggler period, beta function, and beam energy, the CLIC design emittances and damping rates may be attained.
50
24 Nov 00
Considerations about the Impedance of the Y-Chamber 
L. Vos Two particular aspects of the impedance of the Y-chamber designed by LBL are studied. The first aspect is the low frequency (inductive) impedance. The second aspect is the possible existence of a resonant mode which has the appearance of a trapped mode. The basic geometry of the Y-chamber is circular but for computational ease a rectangular geometry has been simulated with MAFIA by B. Spataro [1]. The results obtained by the simulation are very interesting and merit further thought and reflection. I will consider the rectangular geometry and try to estimate analytically the low frequency impedance. I then consider the possibility of a trapped mode in the same geometry. I conclude by making impedance predictions about the (real) circular chamber which cannot be carried out with simulation programs according to our present understanding.
49
8 Nov 00
BPM resolution and beam threading in the LHC
L. Vos The threader in MAD-8 has been used to study first turn conditions for different values of the BPM resolution, the quadrupole alignment error, with and without correction of the magnetic field errors.
48
7 Nov 00
Effect of b3 Error on Nominal and Resonance-free Lattices with Gradient Errors
D. Kaltchev We compare de Nominal and Resonance-free LHC lattices with imposed field errors from table Einj.9901, gradient errors included, on the basis of their dynamic aperture (MAD8) and driving terms (code SODD). The beta-mistmatch and ring tune shift are corrected via the insertion quads. The goal is to test the potency of the resonance-free scheme to cancel alone the effect of the b3 error and to confirm its resistance against the b2 error. Without the 3-order spool correction, due to the systematic b2 changing its sign from inner to outer octant, the optic quality for Beam 1 and Beam 2 is different.
47
27 Oct  00
Threader and BPM's accuracy
A. Verdier The BPM's accuracy for a first turn is evaluated as a funciton of the threader performance.  It appears that it is useless to request an r.m.s. accuracy better than 1.5.mm.
46
17 Oct 00 Do we need to be afraid of the trapped modes in the liner?  L. Vos Special topic presented at the SL-AP Thursday Meeting held on October 12th.
45
26 Sept 00 Effect of a static misalignment of the CLIC BDS A. Verdier The tolerances on the transverse stability of the focusing magnets of the Beam Delivery System of CLIC are in the nm range.  The question addressed here concerns a different aspect of the problem, i.e. the absolute alignment and its compensation.  The effect of static misalignments have been compensated by means of steering dipoles which act both on trajectory and dispersion correction.  Thanks to the correction, the toleance on this misalignment is less tight than the tolerance on stability.  However, because of the emittance buildup associated with synchrotron emission, the tolerance on static misalignment is found to be in the sub-micron range.
44
24 July 00 A study of the dynamic aperture of the LHC at injection with shifts in central beam momentum R. Burgess We present a short study of the dynamic aperture and some discussion of the chromatic properties of LHC optics V6.0 with shifts in the central beam momentum. Within the momentum window defined for the LHC of Delta-p= + 2 x 10^3 the 1000 turn dynamic aperture shows an average reduction of approximately 71.4% compared to the on-momentum dynamic aperture.
43
3 May  00
Geometric Aspects of the Modeling of the Main Dipole of the LHC. 
E. Wildner The input for the optics program MAD is generated from a database that contains information for all elements in the machine, including geometric positioning of the elements. For optics calculations we need for each element its position along a coordinate axis (the "s-coordinate") which means something only if it is coupled to the model of the bending magnets chosen in the program. This note evaluates the geometric consequences of changing the model of the main bending magnets, while keeping the same s-value position for all elements in the machine. Some indications of how to get around the problem are given.
42
12 May  00
Geometrical errors for MQ, MB and BPM for C.O. studies 
J.B. Jeanneret As intermediate short review of the geometrical errors for MQ, MB and BPM is made to allow for closed orbit correction evaluation. 
41
12 May 00
Electron capture in Pb-Pb collisions and quench limit 
J.B. Jeanneret In heavy ion collisions, slightly inelastic electromagnetic processes have cross-sections much larger than hadronic processes. Among these processes at least one, the e+e- pair production followed by the capture of the e-on an atomic shell of one of the ions can induce distant losses of the ions. In the case of Pb-Pb collisions, we show that with nominal luminosities, the quench limit is nearly met in the dispersion suppressor. 
40
22 Mar 00
Tool for calculating the width of resonance islands from maps
L.H.A. Leunissen A semi analytical tool is available to calculate the strength of resonance islands from maps. It is an extension of an existing tool run_tunrescor as reported in [1], [2]. In contrast to pure analytical methods [3], this is unlimited by approximations. Also, islands widths can be calculated for 4D coupling resonance with run_tunrescor_island. The location of the file is: $AP_GROUP_DIR/share/grr/.
39
7 Feb 00
Selft consistent beam-beam for round beams
A. Verdier The linear part of the beam-beam interaction can be computed in a self consistent way for round beams. It is shown that this interaction does not induce any linear instability, in opposite to old naive calculations. The change of both beam size at the crossing and xi_bb are negligible for LHC.
38
13 Dec 99
Software Activity in 1999
F. Schmidt et al The software development on the various FORTRAN software tools are summarized. Possible implications for MAD are stated where applicable.
37
2 Dec 99
Tool for calculating the strength of resonance from 5D maps
P.L.H. Leunissen et al A tool to calculate the strength of resonances from maps. The location of the files is: $AP_GROUP_DIR/share/grr/.
36
2 Nov 99
Possible Phase-advance per cell for Resonance-freeLattices
D. Galletly, A.Verdier Most of the systematic non-linear resonancesassociated with a part of an alternating gradient machine composed of Nc identical cells can be avoided by a correct choice of the two phase advancesper cell. A description of how to calculate these values, and various interesting values of phase advance are given here. A short tracking test shows the interest of lattices obtained by this procedure.
35
22 Oct 99
Test of Geometry Calculations in MAD Version 9
J.M. Jowett The new MAD Version 9 includes calculations of the machine geometry built up from the description of the sequence of elements. These are tested by comparison with MAD Version 8 using the example of the LHC.
34
3 Aug 99
Statistical significance of dynamic aperture calculations
H. Grote The confidence limits for the dynamic aperture calculations are derived independent of the underlying distribution of the values calculated with Monte-Carlo simulations. To have a 95% confidence that only 5% of the total number of all possible LHC realisations have a dynamic aperture value lower than the lowest one found by particle tracking one needs an unbiassed sample of 59 realisations of the LHC with magnetic field errors.
33
16 JULY 99
Physical Constants, Notations and Units for Accelerators Physics
R.T. Burgess, J.M. Jowett, This note is the documentation for a Mathematica [1,2] package designed to provide symbols for physical constants commonly occurring in accelerator physics. The properties of these symbols include their values and units in a very natural way. In addition the package provides capabilities for painless conversions between many systems of units and for checking that the dimensions of expressions are consistent. Basic use of the package is via a palette of buttons that will appear on your screen when you load it. 
32
22 June 99
From Loss-less Oscillator to Landau Damping
L. Vos Copies of transparencies presented in a one day Thinkshop concerning possible detection of Gravitational Waves with the LHC.
31Rev
5 Nov 99
More about a3 syndrome
A. Verdier This note is a compilation of what was published in the beam-physics note 31 (providing missing informations concerning the chromatic coupling on resonance-free lattices), corrections of this note by S. fartoukh and further computations resulting from discussions with J.P.Koutchouk and S. fartoukh. It is intended to provide a basis for further discussion on the usefulness of the a3 correction system.
31C
11 June 99
Correction to the beam-physics note 31: More about a3 syndrome
A. Verdier This note is intended to correct both wrong and missing information in the beam-physics note 31. The latter must not be quoted without a careful check of the correction below.
31
11 June 99
More about a3 syndrome. See also 31C and 31 Rev 
A. Verdier In the presentation of the effect of the a3 uncertainty to the LHC MAC to justify the a3 compensation system, two points were missing: the probability of the "worst case" and the solution to the problem with resonance-free lattices. The aim of this note is to make this information available.
30
2 June 99
About the "ATL" 
A. Verdier The "ATL" predicts that "ground points perform Brownian motion characterised by the variance of the relative displacement which scales as a product of temporal and spatial intervals" This law was mentioned at the beam-beam workshop as a reference to describe the relative motion of magnets. This is critically examined here.
29
23 May 99
Not published yet
J-B. Jeanneret .
28
23 April 99
Beam-Beam effect in LEP, an alternative point of view..
A. Verdier The luminosity data provided by Helmut Burkhardt have been interpreted in term of self-consistent beam-beam element. Single particle parameters have been calculated with MAD including this element. It appears that the actual vertical emittance tune shifts shows that a possible origin of the beam-beam limit could come from Q_x being close to an half integer. A maximum xi_y of 0.111 is predicted for operation at 96GeV according to this consideration.
27
8 April 99
Ripple data 
A. Verdier The effects of power converter supplies ripples measured in the ISR, Spp-S and HERA have been compiled. They can be used to produce tolerances for LHC.
26
17 Mar 99
Equivalence classes of beam-beam encounters in the LHC 
J.M. Jowett This note shows how to sort out the large number of beam-beam encounters between the bunch trains in the LHC into equivalence classes within which bunches see identical sequences of beam-beam encounters. This makes it easy to produce statistics of the encounters and to pick out a representative set of bunches for simulation purposes.
25
16 Mar 99
VLHC accelerator physics workshop 
E. Keil I took part in the VLHC accelerator physics workshop on 21 to 25 February 1999 at the Abbey Resort in Fontana on the shore of Lake Geneva, Wisconsin, USA. It was attended by some 33 people, mostly from FNAL. I was the only person from CERN. The organizers had hoped for more participants from CERN. The home page of the VLHC study collaboration at vlhc.org/ is a useful source of information. It will also have links to the proceedings. FNAL is in the unfortunate position that it will lose the lead at the energy frontier once the LHC experiments produce statistically significant results. Therefore, they want their VLHC studies to be open and visible, and invest funds and manpower. They have great hopes in their next director, Michael Witherell from UCSB. P. Debenham DOE took part in the whole workshop. D. Sutter and another fellow from DOE came for the summary session. Sutter's programme finances part of the magnet development. He tries to push the field to 20 T.
24
15 Mar 99
Magnet error tables from Oracle via the WEB 
E. Wildner The magnet error files used by MAD can be obtained directly from the ORACLE Database via a Web interface. This is a description of what these files contain and how to generate them for use by MAD.
23
5 Mar 99
Constructing Beam-Beam Encounters for the LHC 
J.M. Jowett This note shows how to build the MAD description of all head-on and parasitic beam-beam encounters of any bunch in the LHC, taking account of the detailed structure of the bunch trains, the differences in arc-lengths, orbits and optics between the rings and the charges of individual bunches. It is based on the calculation of the collision schedule described in [1] and related technical documents [2]. Where beam-beam encounters occur inside thick optical elements, these are split appropriately by an automated sequence-editing operation. This is a preliminary version: it cannot illustrate the full process until the optics of Ring 2 is available. All places where modifications are needed are marked in red.
22
1 Mar 99
Beam Losses and Collimation in VLHC 
J.B. Jeanneret, E. Wildner  This note contains the slides of a presentation at the VLHC worshop in Wisconsin in February 1999. We presented LHC data extrapolated to 100 TeV for energy deposition in magnet coils per proton lost, quench limits, estimated transient and steady losses and needed collimation performances. A nearly optimum collimation system is described, with space reservation in dedicated straight sections. We showed that single diffractive interactions in collision induce critical losses in the dispersion suppressors near experimental insertions, which require a local momentum cleaning This would also offer the possibility to do single diffractive physics not feasible otherwise. Our participation to the workshop was virtual and we thank N. Mokhov who presented our slides.
21
24 Feb 99
Collision Schedules for the LHC
J.M. Jowett  This note provides the full technical background to LHC Project Note 179. It includes an extensive pedagogical exposition of the collision schedule problem and its solution, illustrated with simple applications. The nominal filling scheme of the LHC is treated in detail. Further applications only need to load a small package file that includes and automatic report generator for alternative filling schemes.
20
11 Feb 99
Shielding by a Thin Resistive Layer - Comments on Beam Physics Note 18
F. Caspers, E. Jensen We are referring to Beam Physics Note 18 [1 ], where it is stated that a metallic coating thin compared to the skin depth is not an effective shield. We believe that this statement is valid only for infinitely long structures. When considering typical geometries for LHC kickers, the finite length must not be neglected. The results for infinitely long structures are correct, but not relevant. With the help of an example it is shown that the current through the resistive layer can in fact be dominant, in which case the resistance of this layer gives a convenient upper bound for the beam impedance. Both numerical simulations and bench measurements confirm this result.
19
5 Feb 99
Distribution functions and stability diagrams with octupoles
L. Vos A simple procedure is presented to compute the two-dimensional stability diagram related to tune spreads arising from octupoles. The excellent agreement with the results in [1] is somewhat surprising and may be of interest to some of us.
18
14 Jan 99
Electro-magnetic Shielding
L. Vos The penetration of electro-magnetic fields through a metal wall with different layers of dielectric is computed from basic principles. The results are confronted with those obtained by B. Zotter [6,7] and A. Piwinski [8] which are very similar. The disagreement between the two approaches is profound. Engineering practice and tests in the laboratory confirm the theory of shielding given in this paper. It is also shown that the interpretation of shielding reported in a recent paper [3] concerning shields in kickers is not correct. .
17
11 Jan 99
How the LEP tunnel geometry favours betatron tunes for LHC 
J.-P. Koutchouk It was shown lately that the LHC dynamic aperture depends significantly on the integer tunes through resonances excited by the field uncertainties (systematic per arc. We show that the layout of the LHC dipoles allowed by the LEP tunnel is such as to make the 10kth azimuthal harmonics of all multipolar field perturbations almost vanish. If flexible enough, LEP and LHC optics could take advantage of this feature to avoid systematic resonances.
16
08 Jan 99
Longitudinal Space-charge 
L. Vos The transverse space-charge effect has been treated in [1]. Longitudinal phenomena related to space-charge in a low energy proton machine have been reported in [2]. Since the transverse space-charge effect is relevant for the SPS at injection energy it is somewhat natural to consider also the longitudinal space-charge effect.
15
05 Jan 99
Phase advance and beam kick cut in a drift space
J.-B. Jeanneret The best phase advance for cutting a kicked beam is computed in usual coordinates for those who do not like, or do not believe, results obtained with normalised coordinates.
14
18 Dec 98
New 6D beam-beam element in MAD8
L.H.A. Leunissen A new beam-beam element for MAD8 is described.
13
15 Dec 98
The self-field calculation in a relativistic bunch
G. Guignard This note is related to the paper "Electromagnetic limitations of an intense charged particle beam" and the possible space charge limitations due to the current density of strongly focused beams in high energy accelerators (H. Riege) . It follows a discussion on the subject (Friday 4th December 1998) and presents one possible method to deal with the calculation of the longitudinal electric field on the axis of a single relativistic bunch. Results are given for a cylindrical bunch of radius a and length lB for both an uniform and a truncated gaussian charge density. The expression obtained with the uniform distribution for the field amplitude at the bunch edge differs from the equation (20) by a factor a/gamma. Since this factor is usually very large for either the LHC of the CLIC beam, it would strongly modify the conclusions drawn about the risk of having beam densities close to the Langmuir-Child limit in future accelerators.
12
15 Dec 98
Le MAD-9 Nouveau est arrive...
C. Iselin New features in MAD-9, Version 9-1.
11
14 Dec 98
Octupoles, Landau damping and feedback: some information from Fermilab
J.M. Jowett A summary of information received from Fermilab about the use of octupoles and feedback.
10
26 Nov 98
Effects of the sextupoles configuration on the performance of the (102o, 90o) optics in LEP
J.M. Jowett The (102o, 90o) optics used in LEP in 1998 had a new sextupole configuration. This led to a substantial increase of dynamic aperture. This note summarises the calculations and illustrates the physics behind this. It also discusses other beam parameters such as the vertical emittance.
9
19 Nov 98
LHC Arc Lengths in Version 6
J.M. Jowett Each ring of the LHC moves from the outer to the inner aperture of the arc magnets in the experimental straight sections. The arc-length distance traversed by a particle is greater in the arcs where it passes through the outer aperture. This Mathematica notebook derives the arc-length slippages from the MAD description. The results are used to build a model of the arc-length differences that can be used to simplify the analysis of the beam-beam collision schedule without introducing any approximation.
8
11 Nov 98
Impedance of the ‘rough’ beam pipe
M. D'Yachkov In order to reduce the reflection of the synchrotron radiation from the LHC beam screen it has been suggested to make the surface of the dipole screen rough by placing small ribs along the screen. In this note we estimate a contribution of the ribs to the low-frequency beam impedance.
7
11 Nov 98
Tolerance to broken orbit correctors in the LHC arcs
J.-P. Koutchouk There are between 0 and 2 LEP orbit correctors becoming faulty every week. In LHC the time it would take to fix them could become significant. The question is therefore raised as to whether LHC could run with missing orbit correctors or whether some remote switching between power converters should be implemented. The number of unknown parameters makes the point rather a problem of judgment. In this mote I argue that redundancy is not necessary but that the BPM system is critical.
6
6 Nov 98
Present situation of the cleaning insertions IR3 and IR7
J.-B. Jeanneret, D. Kaltchev, A. Verdier,  We analysed and matched many different optics for the collimation insertions IR3 and IR7 of LHC. In each insertion only one case emerges which offers good properties for collimation. This option is also interesting in that sense that it simplifies the hardware of the dispersion suppressors.
5
6 Nov 98
Constant Term in the Detuning with Amplitude due to Sextupole
F. Schmidt Constant Term in the Detuning with Amplitude due to Sextupole is discussed.
4
27 Oct 98
Comparison of LHC Optics Versions 5 and 6
J.M. Jowett This notebook is a follow-up from OpticsCheckOut.nb distributed as Beam Physics Note 3. It takes two similar LHC optics, namely Versions 5 and Version 6, and goes through a sequence of comparisons. More checks and calculations can be added in the framework as required; suggestions are welcome.
3
27 Oct 98
Checks on LHC optics V 6.-2
J.M. Jowett This document takes an LHC optics and goes through a sequence of standard checks and validations. Its content is not meant to be definitive. Its purpose is to provide a framework in which more checks and calculations on any future version of the LHC optics can be added as required. Suggestions are welcome.
2
2 Nov 98
Field in a pill box cavity with thin conducting layer at r = a
G. Dôme We consider a perfectly conducting pill box cavity with a very thin resistive layer much thinner than the skin depth at the beam pipe radius r=a. The integral equation corresponding to excitation by a particle beam is derived and discussed, showing that penetration through the resistive layer takes place only at the resonant frequencies of the coaxial cavity modes.
1
21 Oct 98
Beam-beam in LHC
J. Gareyte Summary of the presentation on Beam-Beam in LHC at LHC Forum of 13 October 1998.