A Primer on Beam Steering. J. Wenninger. Steering algorithms MICADO SVD Bumps And some more… Selected features of the steering program Special steering issues for the SPS. Trajectory/orbit perturbations.
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The position change ui at an element labeled by i due to a kick at an element labeled by j is given by :
where, for the uncoupled case (H and V planes independent) :
A kick only affects downstream elements !
SPS ring H plane – kick at MDH.622
CNGS transfer line V plane,
no effect upstream of the kick..
A change of the correctors by Dqj leads to a position change :
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 :
By minimum I mean that the norm ( r.m.s.) is minimized :
Steering consists basically in solving this LINEAR equation !
Effect of the 1rst corrector
Checkbox defaults depend on the line/ring!
Kicks before, difference & predicted kicks after.
Position before, predicted difference & predicted result
Corrector results in text form
De-selection of iteration 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’
For every correction type based on iterations, a plot showing the evolution of the position and kick rms is automatically produced !
P= x1e1 + x2e2
P= x’1e1 + x’2e2
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.
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 individual corrector responses do not form an ORTHOGONAL basis of the monitor space !
Is it possible to find a basis of the corrector space (by mixing correctors) such that a transformation by R preserves orthogonality ?
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.
The larger wj, the more efficient the eigenvector !
Sorted eigenvalues for the SPS and LHC rings.
There are as many solutions as correctors !
SPS H plane
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 !
As the eigenvalues decrease, the associated eigenvectors correspond to increasingly local ‘structures’
The eigenvectors described on the previous slides are stored in the columns of Z and V
‘pseudo-inverse’ of R
A MICADO correction with all correctors or an SVD correction with all eigenvectors yield the same result !
An easy one for MICADO : the kick is located at the first iteration
A trivial ‘extension’ is the ‘½’ 4-corrector bump that is used for orthogonal steering (angle & position) at targets & splitters, for first turn corrections.. :
Select a BPM from the DV as target for the bump.
Select any element of the optics as target for a bump.
Region of interest
For such a scheme to work, it is necessary to ‘kill’ the leakage by matching the boundary conditions.
The ‘Short Length’correction developed for LEP by T.Limberg/W. Herr solves the problem using a neat idea:
Region of interest
Region of interest
Virtual kick q* at virtual phase and beta
This following slides are not an introduction to the application, but a presentation of some special features that are useful to know !
Edit status of elements by table.
Edit status of elements through the DV.
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 steering).
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 !
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
Custom rules for advanced users
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. 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 !
This allows you to reload the settings for a time that is different from the acq time…
Be patient !
May take some time (~minute)
Extracts a snapshot of all functions from the DB
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 !
Select a channel and click on the ‘Int. Gains’ button. This opens a panel that indicates the channel mapping for the device.
For high intensity (> 1.5 1013) the integral gain should be LOW !!
All those channels share the same integral gain !
Select one or more channels, and click on the ‘Profile’ button to open a display of the selected profiles
Example for all horizontal profiles in TT20 T2
Target autopilot setup
FT autopilot setup
Ring (sext 1 & 2)
Default autopilot tolerances
Check the box if you want to see the fit details..
Small change in sextant 4…
LABVIEW application available from console manager, Equipment Control, BI.
Beam (SFTPRO 2 batches)
Trigger on prepulse
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 !
The SPS orbit is corrected best with few correctors !!
Free choice of time
Choice of time limited to incorporation rule times (checked).
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.
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.
Effect of a small kick on a V corrector at the beginning of TT20 : the trajectory excursion ‘explodes’ near the splitter !