Date: Fri, 14 May 2004 11:08:12 -0400
From: Kirk T McDonald
To: Bill Sands, E-166 List
Subject: Notes from meetings of 5/6-11/04

This lengthy note summarizes my recollection some of the main points from meetings on 5/6 and 5/11, on the E-166 gamma line, and on the positron spectrometer.
I have posted various drawings on the web:
The 3MB .dwg file
The 30MB .dxf version, supposedly readable in AutoCAD 2000:
Top, side, and front views of the baseline spectrometer:
3 sets of first-order ray tracings, showing the possible merit of reducing the offset distance of the dog leg in the spectrometer:
Issues in the spectrometer design include:
-- Reduce diameter of the flux return of the first solenoid to 8.4", so that it doesn't interfere with the mover for the momentum slit.  The coil of the solenoid remains the same
-- Reduce distance between the 2nd bend magnet and the positron reconversion target.
-- Reduce the offset of the dog leg in the spectrometer.
The 2nd and 3rd issues have impact on the rejection of background gammas, => would like to have input from Roman on this....
Now the lengthy notes:
1. Gamma line
A.  The positron production target in the gamma line is to be preceded by a 3-mm ID collimator, some 75-80 radiation lengths
This is to be made from blocks of tungsten about 25 rad len long, and 60 mm in diameter.  One such block is on site, but 2 more must be ordered (or 1 block 50 rad len long.
=> If you wish me to write a Princeton PO for this, please advise.
This collimator will be just upstream of the 80-rad-len lead wall. 
That wall will have a 1" square hole.
The 3-mm-ID collimator WILL BE IN AIR.  The vacuum of the gamma line will terminate in a 1-mil-thick SS window.  Similarly, the vacuum of the positron spectrometer will begin with a 2nd such window, just downstream of the 80-rad-len lead wall.
The collimator will be mounted on a stand that permits manual adjustment of x and y over a small range.  There will NOT be remote adjustment capability.
The 3-mm-ID collimator will have an aluminum oxide screen on its upstream face (with a 3-mm ID hole).  The screen will be viewed by a TV camera.  The foil of the OTR (just upstream of the undulator) will be inserted into the 50-GeV electron beam to generate an intense gamma beam (with the same alignment as the undulator photon beam) to diagnose the position of the gamma beam at the collimator.  The trim magnets HC7 and VC7 will be used to steer the gamma beam onto the collimator.
B.  E-166 will implement its own version of the gamma vacuum line beginning just downstream of the SPPS "sphere".  A 1/4" ID collimator (also used in E-164) will be mounted on a manually adjustable stand at the beginning of the E-166 specific part of the vacuum line.
We desire the windows in the gamma line around the SPPS "sphere" to be removed during E-166 running.
A 2nd collimator, with 1/2" ID is available from E-164.  It was mounted where the FFTB tunnel narrows down.  It would be helpful to install this collimator for E-166 as well.
The rest of the E-166 specific gamma line will consist of 1.5" SS tubing, with 2.75" Conflat flanges.
C.  I think that the E-166 gamma line will actually be above the E-164 gamma line, as the hard-soft bends will kick the electron beams UPWARDS before the 7 permanent dump magnets kick it downwards.
2. Positron spectrometer
A.  Princeton will build the spectrometer magnets, but is hard pressed for time to build the vacuum chamber for these magnets.  SLAC will take over design and fabrication of this vacuum charge, starting June 1.  Princeton will pay for components that need to be purchased from outside vendors.
B. The cable trays on the south wall of the FFTB tunnel will be moved 6-8" south, so that there is an option to have the dogleg beamline as much as 24" south of the gamma line.  This would make it much more practical to implement a solenoid lens(es) between the two 90-deg bend magnets, should the resulting improvement in the quality of the beam transport be deemed critical at a later date.  Certain features of the vacuum chamber, as noted below, will be modified for easier implementation of the possible additional solenoid lenses.
C.  The vacuum chamber can readily be fabricated from stainless steel at SLAC, and it is Dieter's preference to do so, unless there is a strong physics case to the contrary.  {In contrast, if the chamber were to be fabricated at Princeton, it would be more practical to make it out of aluminum.]
D.  The vacuum chamber will begin with a 1-mil thick SS window, following the air gap in which the 3-mm-ID collimator is placed.
E. The positron production target is next in line.  This will actually be a movable set of small disk targets, in vacuum.  The motion stage for this could be mounted vertically upwards.
F. The focusing solenoid as presently specified by Alexander has a diameter of 9" -- which means that it would conflict mechanically with the momentum slit mover.  I propose to reduce the diameter of this solenoid to 8.4".  This can be done by reducing the thickness of the iron flux return from 5/8" to 3/8" with no loss of magnetic performance. 
A 1.6" diameter vacuum pipe passes through the solenoid..
To permit removal of the solenoid from the vacuum chamber, this pipe will not be welded to the entrance face of the vacuum box of the first bend magnet, but will be attached with a "Wilson joint" => O-ring seal.
G.  To make the bend magnets as close to ideal 90 deg sector magnets as possible,
it appears useful to implement a gradient to the pole faces => they are sectors of a cone.  Some work still needs to be done to optimize this, but a first calculation indicates that the pole tips should wide from 2" at the inside corner to 5" at the outer radius.
The pole tip will be detachable, and are the last items needed in the assembly of the magnets.  Hence the details of the pole tip design are not yet on the critical path.
H. The jaws of the momentum slit will be mounted as close to the downstream face of the first 90-deg bend magnet as possible.  The vertical thickness of the pole tips of the bend magnets will be increased so as to permit a more upstream location of the momentum jaws.
The jaws will be thick enough to range out 10 MeV/c positrons.
The jaws will be electrically insulated from the vacuum chamber, and will be connected to a BNC feedthrough, permitting their use as Faraday cups.  (A high-value safety resistor to ground should, of course, be added.)
I.  The section of the vacuum chamber between the two bend magnets will be attached via a pair of flanges with O-rings.
J. I believe the loss of positrons after they pass through the momentum slit will be reduced if the distance between the two bend magnets is reduced  => the offset of the beamline should be less than 18", as determined by possible conflict between the iron core solenoid and the movers for the momentum jaws.
[In case that a 2nd/3rd  solenoid lens is implemented between the two bend magnets, the distance between the two bend magnets should increase.  A 24" offset of the dog leg is foreseen in this case.]
K. The output tube of the vacuum chamber will be 1.9" OD, and will extend up to the location of the positron reconversion target.  This tube will include a tee, into which a movable Faraday cup can be mounted , in vacuum.  The distance from the 2nd bend magnet to the reconversion target should be kept small.
The present drawings still show a vacuum snout extending into the iron-core magnet.
I continue to believe that this is the proper thing to do:
We have to hold the reconversion target at the end of some kind of tube.
There is little/no experimental functionality to performing "target out" runs.
=> simplest to extend the vacuum pipe up to the reconversion target.
APPENDIX: Optimization of the physical length of a solenoid lens of a given focal length.
A "thin" solenoid lens of length L has a focal length f given by
f = 4 lambda^2 / L    ("short" solenoid, L << lambda << f)
where lambda = Larmor distance = c P / e B = P[Mev/c] / 300 B[T] for lambda in meters.
As discussed in my note
a "long" solenoid is well suited for the kind of point to parallel focusing that we need in E-166.  In this case
f = L = pi lambda      ("long" solenoid)
The physical solenoid has windings of length L, inner radius r_min, and outer radius r_max.  The copper has resistivity rho, so the resistance of the coil to solenoidal currents [whose average length is l = 2 pi r_ave = pi (r_max + r_min)] is
R_short = rho l / A = rho pi (r_max + r_min) / L  (r_max - r_min)
   = [rho / L] [ (r_max + r_min) / (r_max - r_min)]
Note that if the short solenoid also has r_min << r_max, then
R_short ~ rho / L
If the total solenoidal current is I, then the power consumed is
P = I^2 R = I^2 [ rho / L] [ (r_max + r_min) / (r_max - r_min)]
An estimate of the magnetic field in the solenoid follows from Ampere's law:
B L = (4 pi / c) I.
That is, B ~ I / L
Hence the Larmor distance at a given momentum varies as
lambda ~ L / I
The focal length of a "short" solenoid therefore varies as
f_short ~ 4 L / I^2 ~ [4 / P] [ (r_max + r_min) / (r_max - r_min)]
or equivalently,
P_short ~  [4 / f_short] [ (r_max + r_min) / (r_max - r_min)]
Further, if r_max >> r_min, the focal length doesn't depend on the solenoid radius either.
Hence, there really isn't any optimum length for a short solenoid -- if we keep the power consumption fixed!
In particular, a long version of a short solenoid is not necessarily a bad thing.
Let us now compare with the case of  "long" solenoid where 
f_long = L = pi lambda ~ pi / B ~ pi L / I.
That is, in my reduced units (rho = 1, c = 1, e = 1, and momentum p = 1), we need I = pi in a long solenoid lens.
The power consumption is
P_long = I^2 R ~ [pi^2 / L] [ (r_max + r_min) / (r_max - r_min)]
           = [pi^2 / f_long] [ (r_max + r_min) / (r_max - r_min)]
Even if r_max >> r_rmin, we find that
P_long / P_short ~ pi^2 / 4 for solenoid lenses of the same focal length.
Although we found no penalty for varying the length of a "short" solenoid" a "long" solenoid does require more power to produce the same focal length.
Hence, we infer that even for a "short" solenoid there is a weak dependence of power consumption on length, with shorter being better.