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					            A Primer on Beam Steering

                           J. Wenninger

            1. Steering algorithms
                • MICADO
                • SVD
                • Bumps
                • And some more…
            2. Selected features of the steering program
            3. Special steering issues for the SPS

5/24/2007                                                  1
            Trajectory/orbit perturbations
  • The trajectory or orbit of a beam is affected by DIPOLE deflections, ‘kicks’
    that are represented by the symbol q.
  • The kick can be due to :
        • Field errors of the (main) bending (dipole) magnets – not all magnets have exactly
         the same field.
        • Misalignments Dx of higher multi-pole magnets :
             • Quadrupoles :      q = K Dx
             • Sextupoles :       q = K2 Dx2
             • ....

  • Quadrupole misalignments are the dominant perturbations at SPS and LHC.
  • Effects of non-linear (> quadrupole) fields can usually be neglected for
    steering linear optics !!! Non-linear fields only contribute at large amplitudes.

5/24/2007                                                                                      2
                          Response to kicks
   The position change ui at an element labeled by i due to a kick at an element
   labeled by j is given by :

                              ui  Rij q j

    where, for the uncoupled case (H and V planes independent) :

               sin( i   j )
                                   i   j                                   A kick only affects
      Rij   i j                                           Trajectory
                                    i   j                                  downstream elements !

            i  j cos( i   j  Q )                      Closed orbit
      Rij 
                    2 sin(Q )

     is the betatron function,  the phase advance. Q is the tune.

    • Note : for Q = integer, Rij diverges for the closed orbit – INTEGER resonance!

5/24/2007                                                                                     3
                                               position ~ i cos(i   j  Q)

                                               • Free oscillation : ‘cos’ term.
                                               • Modulated in amplitude by 
                                                 (local optics).
                                               • ‘Kink’ at location of the kick.

          SPS ring H plane – kick at MDH.622

CNGS transfer line V plane,
no effect upstream of the kick..

• Free oscillation starting at the kick.

   5/24/2007                                                                       4
                                Optics issues
  • If the optics is known, it is easy to evaluate the effect of a kick !
  • The steering program uses the betatron functions, phases… stored in the DB
    to reconstruct the R matrix.
  • Global corrections (MICADO, SVD) work quite well up to beta-beat (error) of
   50%, breakdown starts around 100% beta-beat.
       • SPS ring has a beta-beat of 10-20% - depends on optics & energy.
  • In general coupling is not an issue at SPS and LHC. Horizontal and vertical
    planes can be handled independently. Exception :
       • TT10 for fixed target beam where the planes are exchanged:
        H plane in the PS  V plane in the SPS and vice-versa (aperture optimization).
        For TT10 the analytic expressions breaks down and a response matrix must be
        calculated numerically with MADX.
       • LHC in the very first days (?). But should be manageable.

5/24/2007                                                                                5
                   The ‘steering problem’
  • We have N BPMs that give us the beam position ui at their location.
  • We have M correctors that can provide deflections qi.
  • We assume that we know the response between BPMs and correctors (Rij).
  • Expressed in vector and matrix format :

                u1            R11   R12 ... R1M           q1 
                                                          
                                                             q2 
              u             R      R22 ... R2 M      q  
             u 2        R   21
                                       ... ... ... 
                 ...             ...                          
                                                             q 
                
               u                                          M
                               R      ... ... RNM 
                N             N1                 

            A change of the correctors by Dqj leads to a position change :

                                        
                                Du  R Dq

5/24/2007                                                                    6
                      The ‘steering problem’
   Given a set of measured beam positions um,i we are interested to find corrector
   kick changes Dqc,j such that the resulting beam position uri is minimized :

                                        
                       um  Duc  um  R Dqc  ur  mimimum!

   By minimum I mean that the norm ( r.m.s.) is minimized :

                                              N
                  ur2,1  ur2, 2  ...  ur2, N   ur2,i  mimimum !  ( r.m.s.) 2
                                              i 1

            Steering consists basically in solving this LINEAR equation !

5/24/2007                                                                              7
        MICADO for non-mathematicians
• MICADO (Minimization Carrees ….) is an algorithm developed by B. Autin and Y.
  Marti for the PS in the 1970’s.
• MICADO solves the steering problem by an iterative search for the most
  effective corrector:
    • The jth column of the response matrix R holds the effect of a kick at the jth corrector
      on the beam position:

           R11      R12 ... R1M                                             u1 
                                                                            
           R21      R22 ... R2 M                                          u 
        R                                                             um   2 
            ...      ... ... ... 
          R                                                                  ...
           N1       ... ... RNM                          Compare to…       
                                                                             u 
                                                                              N
                       Effect of the 1rst corrector

   • MICADO compares the response of each corrector (column of R) with the measured
     position. It scans through the correctors to find the one with the closest pattern, i.e.
     that will lead to the largest reduction of the residual r.m.s.

5/24/2007                                                                                       8
                         MICADO iterations
     Iteration 1 : find the most effective corrector. Compute its kick and the residual position.
     Iteration 2 : find the most effective corrector (for the residual position) among the
     remaining M-1 correctors. Compute its kick and re-evaluate the kick of the first corrector.
     Compute the residual.
     Iteration K : find the most effective corrector (for the residual position) among the
     remaining M-(k-1) correctors. Re-compute its kick and re-evaluate the kicks of the k-1
     first correctors. Compute the residual position.

  Note :
   At each step all kicks are re-evaluated to find the best COMBINED solution !
   Once a corrector is selected, it is never deselected.
   As a result of the kick re-evaluation, it is possible that a kick that is selected initially is
    set back to 0 at iteration K !

5/24/2007                                                                                             9
                         MICADO features
     MICADO is very efficient to find isolated (large) kicks.
     MICADO can be fooled by measurement errors (noise, offsets) : MICADO may
     not find the kick at the correct place, but at a phase of ±180 degrees with
     respect to the ‘exact’ location.
     MICADO is sensitive to bad response matrix structures due to missing BPMs,
     bad design of the machine… To avoid numerical problem one can ‘recondition’
     the matrix to detect possible candidates for numerical problems and ‘remove’
     Be careful when using MICADO with a very large number of correctors (for
     example > 20 correctors @ SPS) :
       • Check the strengths to avoid excessive deflections from noise, offsets….
       • It is always possible to correct iteratively:
            • Pick a few correctors, send them.
            • Continue on the resulting orbit with another coupled correctors.
            • Etc…

5/24/2007                                                                           10
                         MICADO in practice

                                       Checkbox defaults depend on the line/ring!

                                            Kicks before, difference &
                                               predicted kicks after.

     Position before, predicted
   difference & predicted result

5/24/2007                                                                  11
    MICADO iterations
     Corrector results    De-selection of iteration
       in text form            info - speed !!
                         (Only significant for LHC !)

                                                        Position results in
                                                         2D + projection
                              Corrector results
                             in 2D + projection

 2D plots show the
 absolute values of
the kicks/positions !
   ‘white = zero’

   5/24/2007                                                      12
            More on iterations

                         For every correction type based on
                            iterations, a plot showing the
                          evolution of the position and kick
                           rms is automatically produced !

5/24/2007                                                13
  • The acronym ‘SVD’ stands for ‘Singular Value Decomposition’.
  • It is an algorithm to invert non-square or singular matrices.
  • In the context of beam steering, the interest of SVD can be explained by
    some of the properties of this decomposition – it is widely used in all modern
    (second & third generation) light sources for feedbacks.

  In the presentation I will give a somewhat ‘un-conventional’ (but without big
   maths) explanation of the way SVD works and why it is interesting…

5/24/2007                                                                            14
                                                                Coordinate systems
                                                             • To describe the coordinates of a point P in space,
                                                               one usually chooses a reference system (e1,e2) that
            e2                          P = x1 e1 + x2 e2
                                                               is orthogonal, i.e. the angle between any pair of
                                                               axis vectors is 90°.
                       e1                                    • In addition the basis vectors are usually
                                                               normalized, i.e. they length is ‘1’ unit.
                                                             • In this example, (e1,e2) constitutes an orthogonal
                                       P = x’1 e1 + x’2 e2     and normalized base of the 2-D space.
                                  P                          • Usually the choice of the reference system is
                                                               arbitrary, or just given for practical reasons
e’2                                                            (simplicity…).
                       e’1             x’1
      x’2                                                    • A transformation matrix can be used to move
                                                               from one coordinate system to another one, i.e.:

                                                                             x1'   x 
                                                                             '   M 1 
                                                                            x      x 
                  x2              P
                                                                             2      2
                                                             • It is also possible to choose a non-orthogonal
                             x1                                reference system – but with the drawback that
                   e1                                          computations become (much) more difficult !

        5/24/2007                                                                                                15
                             Position and corrector space
     In the context of beam steering, we have a position and a kick space, both of very high
      dimension (N and M). The two spaces are coupled by the response matrix R.

                  u2                                              R   q2



                             monitor1   u1                                          corrector1   q1
        The ‘heart’ of the steering problem : orthogonal directions in the corrector space are
         transformed into non-orthogonal direction in monitor space by R (and vice-versa…) !!
        This is due to the accelerator lattice that couples the responses !!

                                                                                       The mathematical difficulty of
                                                                                    steering is due to the fact that the
                                             R                                      individual corrector responses do not
                                                                                    form an ORTHOGONAL basis of the
                                                                                                monitor space !

             monitor1                            R                    corrector1

5/24/2007                                                                                                           16
                        Orthogonal responses ?
    Question :
     Is it possible to find a basis of the corrector space (by mixing correctors)
     such that a transformation by R preserves orthogonality ?



                            monitor1           R                   corrector1

     Answer :
     YES it is possible – this is what SVD does for us !!!
     The price to pay: instead of working with single PHYSICAL correctors,
      one will have to work with mixtures of correctors.

5/24/2007                                                                           17
  • The SVD decomposition builds corrector combinations that are often referred
    to as ‘eigenvectors’ of R (although they are not really in the mathematical sense):
                    v1 j                                    z1 j 
                                                            
                v2 j                                     z2 j 
              vj           with      R v j  w jz j  w j  
                     ...                                       ...
                                                            
                   v                                       z 
                    Mj                                      Nj 

   • The M solutions (as many as they are correctors) have the desired property of
     being orthogonal and normalized :
          v j for the corrector space (they form a complete base of the space)
          z j for the monitor space

   • The ‘eigenvalues’ or ‘weights’ wj is proportional to the r.m.s. position change
     obtained by applying the corresponding corrector eigenvector:
                                         w
            rms (R v j )  w j rms (z j )  j
              The larger wj, the more efficient the eigenvector !

5/24/2007                                                                              18
                        SVD decomposition examples
                                                                            Sorted eigenvalues for
                                                                           the SPS and LHC rings.
                                                                              There are as many
                                       SPS H plane                         solutions as correctors !

                                                                      Ratio max/min ~ 100
                                                                      Very regular lattice !

                                         LHC H plane – 2 coupled rings – IR1&5 squeezed

Ratio max/min ~ 10’000
‘Near singular’ solutions
    in the LHC IRs

                              ‘Singular’ solutions (i.e. very poor ratio reponse/kick
                                 strength). Can lead to problems for MICADO !
      5/24/2007                                                                                 19
 Eigenvectors examples : LHC

No. 1

        No. 137

                               As the eigenvalues decrease,
                               the associated eigenvectors
                                correspond to increasingly
                                     local ‘structures’

            No. 516

 5/24/2007                                            20
                         Corrections with SVD
                                                                      u1 
                                                                      
1. The position measurement is decomposed uniquely into the        u2  N 
   monitor eigenvectors. The residual is the un-correctable      u      c j z j  residual
   part of the measurement.
                                                                       i 1
                                                                     u 
                                                                      N
2. The coefficients cj are obtained from a very simple and                N
   very fast operation (know as ‘scalar’ product).                 c j   u k z j ,k
                                                                         k 1

3. The same cj are used to compute the correction kicks Dq,
   because there is a direct correspondence between the
   eigenvectors vectors in position and corrector space. The                       K
                                                                                           cj 
   correction may use between 1 and N eigenvectors (the ‘user’            Dq               vj
                                                                                    i 1   wj

Note : the number of eigenvectors controls how ‘local’ the
 correction will be:
     • Few eigenvectors  corrects only global structures.

 5/24/2007                                                                                         21
                             SVD more formally…
   • In mathematical terms, the SVD algorithm decomposes matrix R into 3
     matrices Z, W, and V :

                                                                       VV T  V TV  1
                      R  ZW V T                  with
                                                                        ZTZ  1

    w1 0       ...  0          v11 v12    ... v1M          z11   z12    ... z1M 
                                                                                 
                                                                                           The eigenvectors described on
    0 w2       ...  0         v    v22    ... v2 M        z      z22    ... z2 M 
W                         V   21                      Z   21                         the previous slides are stored
     ... ...    ... ...          ...  ...   ... ...           ...   ...    ... ...        in the columns of Z and V
   0 0                                                                           
               ... wM 
                                 M 1 vM 2   ... vMM 
                                                               N1    zN 2   ... z NM 

     • The correction using k eigenvalues is given by :                                 1 / w1 0   ...    ... ... 0 
                                                                                                                     
                       ~1                                                            0     ...  0     ... ... ...

          Dq  VW Z um  R um1    T                                                     ...   0 1 / wk   ... ... ...
                                                                                 W 1                               
                                                                                         ...        0     0 ... ...
                                                                                         ...                  ... 0 
                                                                                                                     
                                                                                         0                ... 0 0 
               ‘pseudo-inverse’ of R                                                           ... ...               

5/24/2007                                                                                                             22
 • Computing speed:
      • The SVD decomposition is CPU intensive, Time ~ (N,M)3 :
                                               SPS ~ 200 ms,       LHC, 2 rings ~ 20 s !
      • The correction itself is very fast :   SPS ~ 1 ms,         LHC ~ 10 ms.
      • As long as the BPM/corrector pattern is constant, decomposition must not be redone.
 • SVD corrections go from global (few eigenvectors) to local correction (many eigenvectors).
      • Not suited to identify few isolated kicks.
      • Can be used to correct few large kicks with a large number of small kicks.
      • Can be configured to be insensitive to bad BPMs (limit to largest eigenvectors).
 • The kick strengths used by SVD tends to increase monotonically as the number of
   eigenvectors is increased:
      • SVD is useful when the corrector strength is limited. Example :SPS at 400/450 GeV.
 • SVD is well suited for real-time feedbacks:
      • Requires less corrector strength.
      • Stable and fast computing time (correction only!).

            A MICADO correction with all correctors or an SVD correction
                   with all eigenvectors yield the same result !

5/24/2007                                                                                       23
            Test case 1 : single kick @ SPS

5/24/2007                                     24
                    Test case 1 : MICADO
     An easy one for MICADO : the kick is located at the first iteration

        Kick convergence                                    Orbit convergence

5/24/2007                                                                       25
                              Test case 1 : SVD
• As this is a single isolated kick, a large number of eigenvectors (~ 100) are required to
  find the single kick.
• With 20 eigenvectors, the correction is ‘reasonable’

           Kick convergence                                              Orbit convergence

5/24/2007                                                                                     26
            Test case 2 : BPM offset

5/24/2007                              27
                     Test case 2 : MICADO
   • With the SPS lattice MICADO jumps on the two correctors around the monitor and
     builds a bump around the bad reading.

         Kick convergence                                        Orbit convergence

5/24/2007                                                                             28
                            Test case 2 : SVD
   • SVD is much less sensitive to the isolated BPM error and it takes a large number of
     eigenvectors (~ 100) to build the same bump than MICADO.
   • With 20 eigenvectors the perturbations are not ‘very’ large.

         Kick convergence                                            Orbit convergence

5/24/2007                                                                                  29
                             Local bumps /1
  • Simple bump algorithms can be used to steer the beam at one location.
  • The simplest bump is the 2-corrector bump:


                                                    • Controls only the amplitude. Angle at
                                                      target depends on local optics.
                                    C2              • Requires perfect positioning of C2.
                                                    • Ad-hoc conditions for 2C bump are
                                                      almost never encountered.


    • The 3-corrector bump is a robust and universal bump:

                                                     • Controls only the amplitude. Angle at
                                                       target depends on local optics.
                                                     • Closure with C2 & C3.
                                                     • This bumps works almost anywhere,
                                                       except for rare phase conditions
                                                       between the correctors.
         C1                   C2         C3

5/24/2007                                                                                      30
                               Local bumps /2
  • The 4-corrector bump gives full control over position and angle:

                 Target                                 • Controls amplitude and angle.
                                                        • Closure with C3 & C4.
                                                        • This bumps works almost anywhere,
                                                          except for rare phase conditions
                                                          between the correctors.

         C1      C2             C3       C4

        A trivial ‘extension’ is the ‘½’ 4-corrector bump that is used for orthogonal
        steering (angle & position) at targets & splitters, for first turn corrections.. :


                   C1     C2

5/24/2007                                                                                     31
                              Local bumps in practice
  • The steering program allows you to build 3C and 4C bumps at any location in any ring or line.
  • But due to the local optics, ‘good’ bumps cannot be build everywhere (missing correctors,
    strange phase advance…) : always check the bump shape and strengths.
         • SPS ring: 3C bumps work much better than 4C bumps due to the 90 phase advance per cell.
         • TT10 with FT beams : due to the coupled optics the algorithms break down in the skew section.

                                                                               • By default the correctors for the
                                                                                 bump are identified automatically.
                                                                               • You can select the correctors
                                                                                 manually: for difficult regions (optics)
                                                                                 or to make more sophisticated bumps
                                                                                 (long bumps…)

Select a BPM from the DV as           Select any element of the
    target for the bump.             optics as target for a bump.

5/24/2007                                                                                                           32
            Bump details
                      A detailed plot of a calculated bump is
                      available from the menu bar:
                        • Location of target.
                        • Correctors.
                        • All elements in optics within bump range.

5/24/2007                                                   33
                             Local corrections
 • Suppose someone would like to correct the position in a region which is
      • larger than a single point  not a bump,
      • smaller than the entire ring/line.

 • If one uses MICADO/SVD just inside the region of interest, the correction will leak out
   into the rest of the ring/line, because there are no boundary conditions:

                  Leakage             Region of interest

         For such a scheme to work, it is necessary to ‘kill’ the leakage
                     by matching the boundary conditions.

5/24/2007                                                                                    34
                    (LEP) Short Length correction
    The ‘Short Length’ correction developed for LEP by T.Limberg/W. Herr solves the problem
     using a neat idea:

Leakage       Region of interest      Leakage                           Leakage        Region of interest      Leakage

                                                   equivalent to
                                                                                         Virtual kick q* at
                                                                                      virtual phase and beta
          • Viewed from the outside, the leakage can be described as originating from a virtual kick q*:
            one could try to close the correction using 2 correctors on either side like a 3C bump !
          • The Short Length correction proceeds in iteration:
               1.Correct within region.
               2.Evaluate q* and the 2 closure kicks (one on each side, selected automatically).
               3.Add the effect of the closure kicks to the correction (affects the inside !!).
               4.Back to 1. until no more improvement.
          • The short length is useful and works rather well in rings (LEP, LHC, SPS [seldom used..])
            where it is sometimes desirable to correct/improve the orbit locally.
          • The short length does not always converge !

   5/24/2007                                                                                                   35
 Steering in transfer lines or on the first turn of a ring (i.e. single pass) is
  sometimes referred to a threading.

 The following options are available from Menu ‘Steering’  ‘Threaders’ (first
  turn/transfer lines ONLY):

 • Single point threading:
      • Move the beam at a selected monitor using a nearby and suitable upstream corrector.
      • Useful in difficult cases to flatten the trajectory along a line – for example TT20.

 • LEP-style threading (‘LEP Threader’):
      • MICADO correction in a selected sub-region of the ring/TL using a maximum of 2
      • Well suited to thread in large machines like LEP & LHC.
      • This is basically a specialized application of MICADO.

5/24/2007                                                                                      36
                                     And more…
 • The effect of a kick of arbitrary amplitude at any corrector can be computed and sent to
   the machine:
       • Test BPM response.
       • Thread beam…

 • Bare corrections can be evaluated with MICADO & SVD. When a bare correction is
   requested then:
 1.   In the first stage, the effect of all correctors is unfolded: this corresponds to the ‘bare’
      orbit/trajectory that one would obtain by setting all correctors to zero (which can be
      done by SW but not always in the real machine !!).
 2.   In the second stage the bare orbit is corrected with MICADO/SVD.
      The interest of the bare correction is that it is possible to reset/reseed the corrector
      settings (for example to clean up in case many correctors have been accumulated…).

5/24/2007                                                                                        37
                   The steering program:
                   a selection of options

 • The steering application for SPS, LEIR (and LHC) is build on top of/integrated
   into the LSA control system.
 • It is an offspring of the LEP/SPS Motif/C steering application that was used
   from 92(?) to 2004:
      • Generic (configurable) core.
      • Machine dependent add-ons.
      • Lot’s of new stuff still to come…

   This following slides are not an introduction to the application, but a
     presentation of some special features that are useful to know !

5/24/2007                                                                           38
            Color conventions for elements
            The following color convention is used for monitors and correctors:

                                                              • HW Error : HW returns an error status.
                                                              • OP disabled : declared bad by OP.
                                                              • Locked : ‘permanent’ OP disable status (DB).

       • The warning status is only used for SEMs at the SPS when the signals are either too
         higher (saturation, gain too high) or too low.
       • Elements with state HW error, OP disabled and Locked are ignored for steering !
       • Locked elements are part of the configuration but are normally not activated (i.e.
         not used in steering algorithms) :
              • Interlocked bending magnets in TI2,TI8,TT41 that are only used during setting up.
              • Special corrector magnet doublets in TT10.
              • Special corrector magnet in the SPS (MDVB.517).

5/24/2007                                                                                              39
                          Status control

                                                   Edit status of elements
                                                          by table.

Edit status of elements
    through the DV.

                                 Editable :
                                 • Position, calibration & offset
                                 • ‘OP Enable’ : OP status flag

5/24/2007                                                                    40
                               Locked elements
 • Locked elements appear in violet in the DV and in the detail tables.
 • They are not used for steering (i.e. cannot be trimmed) and cannot be re-enabled using the
   standard selection.
 • Can be unlocked in menu ‘Status-Control’  ‘Status Control Tools’  ‘General Tools’. Make
   sure you know what you do before activating such elements !

  Example of the TT10 corrector magnet doublets : 2 correctors side-by-side (ramp speed) with individual
  PCs. The deflections should be shared equally among both correctors (taken care automatically by the

5/24/2007                                                                                                  41
            Corrector calibrations & status
                           This program uses exclusively ANGLES for steering
                                            – no currents !

                                         Edit status of elements by table.

                     Watch OUT : Some correction elements have a calibration of -1 !!

                  This is the case for BENDING magnets (as opposed to CORRECTORs) and
                   is due to a different SIGN CONVENTION for deflections in MADX !
                                          Don’t change such signs !

5/24/2007                                                                               42
            Data sets
                • There are presently up to 7 datasets (monitor
                  readings + corrector settings) in memory at
                  the same time.
                   • The ‘active dataset’ is the dataset that is
                     shown in the DV!
                   • The predictions of the last corrections are also
                     stored in separate dataset (for comparisons…).
                     • CNGS ‘special’ – 4 additional sets:
                         • Transfer no 1. & no 2.
                         • Average Transfers 1 & 2.
                         • Difference Transfer 1 & 2.
                • The datasets can be
                   • loaded into the DV (as they are or as
                     difference wrt reference).
                   • used as reference dataset.
                • To come soon :
                   • Post-mortem dataset (for selected
                   • Not just the last, but the last N (5,10?)

5/24/2007                                                          43
                      Trim Incorporation
 In a pulsed machine like the SPS, it is not sufficient to calculate a correction
  for a given time in the cycle tc, but it is also necessary to define how such a
  change is propagated to earlier and later times:


                                             DK / DI


  • The propagation of trims inside a cycle is designated as ‘trim incorporation’ –
    and this does not just apply to steering…
  • The way trims are incorporated is normally defined in the LSA DB.

5/24/2007                                                                             44
                          Incorporation rules
 • Default incorporation rules are defined for all particle transfers of the SPS.
 • For transfer lines the rules are simple : a flat function !
 • For the SPS ring, the default DB rules can be displayed from menu ‘Trim’  ‘Incorporation
   & Skeleton’ :
                                                                 Custom rules for
                                                                  advanced users

5/24/2007                                                                                      45
     Trims – how to send to HW     New (and not finished) : an
                                  internal history of the trims
                                      that have been sent !

List of elements that will be
   trimmed (from the last
    calculated correction)

                                 The incorporation rule that
                                        will be used…

            • A correction can be send as many times as desired to the
              machine, and multiplied by any factor.
            • The trims are always ADDED to the existing functions.
            • There are 4 different ways to send the trims.
            • The trim is based on the LAST calculated correction.

            A. Increment functions by 100% of correction.

                     Indicates the total increment.

            B. Increment functions by selected % of correction.

            C. Increment functions by factor x correction.

            D. Increment functions such that the total trim is
               factor x correction.

                        Equivalent to A. – direct send to HW

                             Direct CANCEL of last trim !

                                  Data catalogs
  The steering program provides 2 simple, file based data catalogs, that can be found in the
   ‘File’ menu:

       • A ‘Data Set Catalog’ :
             • Data files contain one acquisition and the associated corrector setting.
             • For references or temporary snapshots.
             • The data sets can be used to re-establish (reload) the corrector settings
               stored in the file and/or reference for corrections…

       • A ‘Settings Catalog’ :
             • Data files contain a snapshot of all steering element functions for a cycle.
             • Data files contain NO monitor acquisition.
             • The data files can be used to restore the functions for an entire cycle.

  Note : It is also possible to roll back settings of one or more elements to an arbitrary time
   in the past using the ‘Trim Archive’ application of Delphine.

5/24/2007                                                                                      48
                           ‘Data set’ catalog
    • The entries of the data set catalog may be reloaded into the DV for display, or as
      reference orbit (to compute differences…).
    • Once the data is displayed in the DV, you can reload the settings into the machine…

5/24/2007                                                                                   49
                        Reloading a data set
    • Any dataset that is loaded as active data set (i.e. is visible in the DV) may be reloaded into
      the machine.
    • Step 1: in menu ‘Trim’ select ‘Settings Reload’, this opens the panel shown below. Select
      the plane and click on ‘Prepare Settings’. The settings difference will be shown in the DV.

                                                                      This allows you to reload the
                                                                        settings for a time that is
                                                                      different from the acq time…

     If you are happy with it…
    • Step 2: You can now handle the settings change like any other correction and send it to
      the machine. It will be handled like any trim, including incorporation rules…
    • Repeat for both planes, or do it just for one !

5/24/2007                                                                                        50
                                  Settings catalog
 • The settings catalog holds complete functions, and you cannot visualize them.
 • You can reload the settings for the H and/or V plane : this will replace the current
   functions by the ones in the catalogs. You can only reload ALL elements of a plane.
 • Works only for cycles with the SAME LENGTH !!

                                                                             Be patient !
                                                                     May take some time (~minute)

     Extracts a snapshot of all
      functions from the DB
5/24/2007                                                                                   51
  • (Most of) the SPS SEMs a ‘IN-OUT’ devices that are normally OUT of beam when not in
    use for steering or profile measurements. A few exceptions concern grids around the
    TT20 splitters and around the targets.
  • For the moment the SEMs must be moved In/Out manually through EquipState.
    Sometimes in the future the In/Out movement will be done automatically by the steering
  • SEM functionality in the steering:
       • Integral and proportional gain setting.
       • Detailed raw data (debugging…).
       • Profiles (for BSGs).
       • Available for :
             • T2Transfer (TT20T2)
             • T4Transfer
             • T6Transfer
             • TT10 (SEM configuration)

5/24/2007                                                                                    52
                                               SEM gains
     • The SEM acquisition hardware provides :
           • An integral gain for a group of 16 channels (values = Low (1), Medium (~10), High (~100)).
           • A proportional gain that can be set individually for each channel (values = 1,2,4,8,16).
           • For each channel Total gain = Integral gain x Proportional gain.
           • The raw data is saturated when it is above 2040.

FESA device (class BESTLD)

  Select one or more
channels, right click to
  get the gain popup.
This will set the gain of
ALL selected elements !

    5/24/2007                                                                                             53
                                 SEM integral gains
 Select a channel and click on the
 ‘Int. Gains’ button. This opens a
  panel that indicates the channel            For high intensity (> 1.5 1013) the
      mapping for the device.                  integral gain should be LOW !!

All those channels share the
     same integral gain !

   5/24/2007                                                                        54
                                  SEM profiles
                          A simple profile display of BSGs is available directly in the steering:
 Select one or more
                               • Mean, sum, rms and emittance estimate.
channels, and click on
the ‘Profile’ button to        • Not fit !
open a display of the
  selected profiles

                                                                     Example for all horizontal
                                                                      profiles in TT20  T2

 5/24/2007                                                                                          55
    • Automatic steering of the beam (Autopilot) is available for:
          • North area target steering on T2/T4/T6: optimize the symmetry.
          • First-turn correction for the SPS ring (transfer SPSInjection).
    • The autopilot panel is available under the ‘Trim’ menu.
    • By default the autopilot stops automatically when the target is reached. Default
      parameters should give good performance. When the symmetry is very low on a target,
      convergence speed can be improved by manual pre-trimming…

  Target autopilot setup                                                      FT autopilot setup

5/24/2007                                                                                     56
            SPS ‘complex’ : special issues

5/24/2007                                    57
                         TT10 : new features
  • For TT10 the steering program provides now 3 different monitor configurations:
       • The configuration with TT10 couplers. This year 6 monitors of TT2 are also visible.
       • A configuration with TT10 SEMs when the couplers do not work (or if you do not trust them…).
       • A new configuration that includes the TT10 couplers and the first two SPS sextants after injection
         (1&2). With this new configuration one can steer TT10 and the first turn at the same time. This
         should become the standard selection. An ‘autopilot’ for the first turn correction (no more knobs !)
         is operational.
  • After selecting ‘SPSInjection’ for a given cycle, the following popup will appear that let’s
    you choose the desired configuration.

5/24/2007                                                                                                  58
                     TT10 with TT2 & Ring
      • Note that we have no control over TT2…
      • Be careful when using MICADO to correct the FT : it will sometimes use dipoles at
        the beginning of TT10 instead of the end, due to the large excursion that we
        frequently have in TT10.

            TT2        TT10                         Ring (sext 1 & 2)

5/24/2007                                                                                   59
                             TT10 : FT autopilot
• The FT Autopilot automatically corrects the first turn (wrt closed orbit) by fitting the
  trajectory in the SPS over the first 2 sextants.
• The fit is less sensitive to individual BPM errors than the traditional correction based on 2
  BPMs/plane (more improvements are foreseen) .
• The fit is extrapolated to a bending dipole at
 the entrance of the SPS (same  both planes).
• An orthogonal steering (1/2 4C bump) is used to
 correct the position with the last correctors of TT10.
• The energy error in the H plane is NOT corrected !

             Default autopilot

                 Check the box if you want
 5/24/2007        to see the fit details..                                                        60
            SPS ring : first turn issues
                                            Beware of 2 traps for first turn
                                             measurements & correction :

                                          • The delay between pre-pulse and first turn
                                            (usually 3 or 4) must be correct. If not, you
                                            get either no data (delay to small) or the 2nd
                                            3rd etc turn. If the FT correction diverges
                                            check the delay. Reduce by 1 until you see no
                                            more beam to find the correct delay.

                     FT-CO example
                                          • For the FT beam, the transverse position (and
                                            therefore first turn) varies along the batch
                                            (5 turn CT extraction). If the 6 BPM crates
                                            are not set up to measure on the same part of
                                            the batch, you can see jumps in the
                                            trajectory between sextants !

             Small change in sextant 4…
5/24/2007                                                                         61
                 SPS ring : MOPOS scope & gates
       LABVIEW application available from console manager, Equipment Control, BI.


                  Beam (SFTPRO 2 batches)
                                                       • It works…but be patient !
                                                       • The trigger is sometimes ‘bizarre’.
                                                       • If there is no beam signal (yellow
                                                         trace), try to increase the time scale
                                                         (bottom left) and then change the
                                                         ‘Trig Pos’.
                                                       • For (single) bunch beams, the falling
                           Gate                          edge of the gate must be at the peak
                                                         of the bunch signal (the sample mode
                                                         must be ‘bunch’, slide 60) .

                                                     Trigger on

5/24/2007                                                                                62
                                      SPS ring
  • The SPS ring has a phase advance of almost 90° per cell. It is a very regular lattice.
  • There are 108 horizontal and 108 vertical corrector magnets. At top energy the correctors
    are weak, with kick limits at 450 GeV of:
             ~ 10 rad in H          bump of ~ 1 mm amplitude
             ~ 20 rad in V          bump of ~ 2 mm amplitude
  • At top energy the orbit is therefore corrected at the startup by realigning the quadrupoles
    such that the rms is < 2 mm at 400 GeV with the FT beam. The drift over the year of the
    orbit is usually < 2 mm rms.
  • The orbit errors at injection and in the early part of the ramp can be corrected with a few
  • At top energy SVD can be used to correct the orbit for MDs. For regular operation we do
    not use the correctors on the flat tops (if they fail we don’t have to worry !!).
  • Note that the tunes are different for FT (26.62,26.58) and LHC beams (26.13,26.18). Due
    to the factor 1/sin(Q) in the closed orbit response, the same misalignment yields a factor
    ~2 larger orbit errors for LHC beams than for FT beams !
    On the flat top the orbit is a factor ~ 2 worse for LHC beams ! Don’t be surprised !!

5/24/2007                                                                                    63
          SPS ring : MICADO with few & many
                                                         Vertical SPS orbit corrected
                                                         with 4 correctors:
                                                         • RMS ~ 1.4 mm.
                                                         • Few outlying monitors.

                                                        The same orbit corrected with 40
                                                        • RMS ~ 0.4 mm – little (useful) gain.
                                                        • No more outlying monitors.
                                                        • But many -bumps (in fact 2C bumps)
                                                          that MICADO uses to steer away
                                                          monitor outliers.

   At the SPS the combination of 90° phase advance per cell and the monitor sampling
           makes it possible to steer away almost every monitor error/offset !
5/24/2007        The SPS orbit is corrected best with few correctors !!              64
                     SPS ring : incorporation rules

• To avoid building spiky functions that the
  PCs cannot follow, (non-MD) corrections at
  the SPS ring follow strict incorporation
   • Flat functions on all plateaus (injection, flat
   • Triangular shapes at pre-defined points for
     the ramp.

• If a correction is attempted in the ramp at
  a time that does not correspond to a
  triangle peak, the correction will be shifted
  in time to the nearest one !
                                                       Free choice of time
                                                          (unchecked !)
• To ensure that you measure & correct at
  the right time, you can limit the acquisition
  time selection using a checkbox in the
                                                                             Choice of time limited
  ‘Acq&HW’ menu.                                                              to incorporation rule
                                                                                times (checked).

   5/24/2007                                                                                   65
                      SPS ring : multiple acquisitions
        In order to quickly check the orbit, the radial steering… for the ramp, or scan the orbit in
         time… a multiple acquisition option is available from the ‘Machine Specials’ menu.

                                                        • Select start time, end time and step.
                                                        • Max. of 80 acquisitions.
                                                        • Able to acquire 10-20 orbit/cycle – be patient !

                                                                  A summary plot of orbit average, rms and
                                                                   dp/p versus time is presented when the
                                                                           acquisition is finished.

 One can click on any orbit in the
list and display it again, and scroll
  through the list with the mouse.

      5/24/2007                                                                                          66
 • TT20 is a tricky line because:
      • Steering depends entirely on SEMs.
      • The beams are split vertically.
      • The very large  function of 20 km (for splitting) makes vertical steering very
        ‘touchy’. If you start optimizing the V steering, it usually takes a while !

                                                   Effect of a small kick on a V corrector at
                                                   the beginning of TT20 : the trajectory
                                                   excursion ‘explodes’ near the splitter !

 • In both planes the best steering is not the one that gives ‘0’ reading on the monitors. In
   fact one often has to be off-center around the splitters because of:
      • Loss optimization (mostly around the splitters !) : BLMs at splitters and intensity.
      • Intensity sharing between targets.
      Note : the more beam there is on T6, the lower the losses…

5/24/2007                                                                                       67
            To find this presentation…

5/24/2007                                68