A scheme to extract a low intensity slow spill Main Injector beam to
the Meson Area without compromising antiproton production rate
October 2000
C. Shekhar Mishra, Thornton Murphy, Rajendran Raja
Fermi National Accelerator Laboratory
Abstract
We propose a scheme to extract a low intensity beam of 120 GeV Main
Injector protons to the Meson Area while simultaneously fast extracting
protons for antiproton production such that the total antiproton
production rate is unaffected.  We achieve this by injecting two
booster batches into the Main Injector.  At the beginning of flat-top,
a single booster batch is extracted to the antiproton source. The
remaining batch is used to provide a slow spill to the meson area of
low intensity.  At the end of the slow spill, the total amount of beam
extracted to meson area is less than 10% of the remaining batch which
is extracted to the antiproton source providing two batches for
anti-proton production in a period of ~ 3 seconds, thus preserving the
rate of antiproton production.
1 Introduction
The current cycle for p-bar production (referred to in this document as
"pure p-bar spill") [1] calls for a 1.466 sec cycle time for extracting
a single booster batch of 5x10^12 protons to the antiproton target.
This results in 2455 proton shots to the p-bar target (henceforth
called p-bar shots) and 1.2x10^16 protons delivered to the p-bar target
every hour.  In the "mixed slow spill mode" as outlined in the Main
Injector Design manual [1] and used in calculating rates in the P-907
proposal [2], one runs a 1 sec slow spill combined with p-bar
production, one has 6 booster batches in the Main Injector, of which
the first is extracted to the p-bar target and the remaining 5 are
resonantly extracted to the switchyard over a period of 1 sec.  In this
document, we refer to the "mixed slow spill mode" as the "single slow
spill", since only a single booster batch is delivered to p-bar per
spill. The cycle time is 3 sec and results in the delivery of 0.6x10^16
protons to the p-bar target every hour.  This is a loss of a factor of
2 in p-bar stacking rate and is clearly unacceptable.  One option is to
run the mixed slow spill cycle after every 10 pure p-bar cycles and
this will result in a loss of 8.7% in the number of p-bar's produced
per hour.  The p-bar stacking rate is a non-linear function of the
total amount of p-bar's stored, so the full impact of running a mixed
cycle after 10 pure p-bar cycles may be less than this.  The amount of
beam delivered to the Meson area will be 17% of what could be achieved
if every cycle is a mixed cycle.
The P-907 TPC is expected to take data at a rate of ~ 60Hz.  Its dead
time is 16 microseconds, the time taken for charge to drift across the
chamber.  During a 1 second flat-top, one expects ~10^5 beam particles
to pass through the TPC and 10^3 particles to interact (for the thin
target part of the experiment).  One booster batch takes 11
microseconds to circulate in the Main Injector.  This implies that it
is possible to generate a secondary beam at the TPC with uniform duty
factor from a single circulating booster batch.  This permits us to
shorten the cycle time of the "single slow spill" from 3 secs to 2.667
seconds, since we need only inject 2 booster batches.
The total amount of beam needed for an experiment such as P-907 is
10^9-10^11 protons per second.  For a slow spill of one second
duration, this is 2x10^-4 to 2x10^-2 of a single booster batch in the
main injector. This permits us to attempt to extract a small fraction
of a single booster batch during flat-top and then reuse the remainder
for p-bar production[3].  For this scheme to work, the slow spill
resonant extraction has to be adiabatic enough so that at the end of
the slow spill, it is still possible to use the remaining booster batch
in the main injector for p-bar production.  In order for p-bar
production to be efficient, the debuncher has to be cleared of
collected p-bar's which takes approximately 1.466 seconds.  This
dictates the length of the flat top.  We refer to this new spill mode
as the "double slow spill".
2 Simulation results
One needs to establish that the emittance of the batch after slow spill
can be made to adiabatically relax to a value suitable for extraction
to p-bar for this scheme to work.  The following section contain
details of the results of simulations done by John Johnstone using the
Main Injector simulation program.  Slow extraction at the Injector is
accomplished through excitation of the half-integer resonance.  Two
orthogonal families of quadrupoles distributed on the 53rd harmonic
provide the half-integer driving term. One family alone produces the
desired phase-space orientation for extraction, while both families are
available to correct the intrinsic half-integer stopband of the
machine.  A third quadrupole family regulates the actual extraction
rate through manipulation of the 0th harmonic (tune shift).  The large
(non-linear) octupole component of the main quadrupoles drives
primarily the 0th harmonic and is sufficient to provide the amplitude
dependent tune-shift (Delta mu ~ x^2) that splits the phase-space into
stable and unstable regions.
The numerical simulation of resonantly extracting low intensity beam
proceeded as follows:
*  Chromaticity was tuned to nu_x = nu_y = +5.  The main quadrupoles
were used to move the fractional machine tunes from their nominal
(.425, .415) values to (mu_x, mu_y) = (.485, .415), placing the
horizontal tune close to the half-integer;
*  The transverse co-ordinates of 1000 particles were randomly selected
from a 20 pi mm-mr (95%, normalized) Gaussian distribution, appropriate
for describing the launch point at mid-quad #516.  Momenta were chosen
from a Delta  p/p = 0.04% Gaussian distribution.  The beam profile can
be seen in Figure 1;
*  Particles were allowed to circulate unmolested for 200 turns to
establish 'steady-state' conditions.  This is a necessary step because
the non-linear nature of the machine distorts the phase-space from the
initially pure Gaussian;
*  One family of 53rd harmonic quadrupoles were ramped over the
subsequent 300 turns to the point where the 20 pi mm-mr emittance
contour was just marginally stable;
*  The 0th harmonic quadrupole circuit was ramped slightly over 1000
turns, causing just 5% of the beam to become unstable, move out along
the separatrix, and get extracted.  The beam profile can be seen in
Figure 2;
*  The remaining 95% of the beam circulated for 200 turns to allow time
for straggling unstable particles to get extracted;
*  Over the next 300 turns the harmonic quads were ramped down to zero;
*  The remaining beam was again allowed to circulate unperturbed for
200 turns to reestablish a steady-state distribution, and;
*  The emittance of the final circulating beam was measured to be 18.4
pi mm-mr (95%, normalized).  The beam profile can be seen in Figure 3.
3 Main Injector results
We have succeeded in testing the simulations with Main Injector low
intensity beams (5E11 protons).  We measured the emittance of the beam
using flying wires when the Main Injector fractional tunes were 0.425
in the horizontal and 0.415 in the vertical.  The results are presented
in figure 4 which measures a horizontal emittance of 9.47 pi mm-mr and
a vertical emittance of 8.14 pi mm-mr, in the first pass of the flying
wire.  The horizontal tune was then changed by turning on the 53
harmonic quadrupoles and the system was taken very close (within .002)
of the half integer resonance.  The emittance at this stage is shown in
figure 5, where the first pass values of the emittance are 17 pi mm-mr
and 8.76 pi mm-mr in the horizontal and vertical respectively, i.e,the
horizontal emittance has doubled.  This is also evident from the beam
profile in the figure.  After keeping the beam for 300 millisecs at
this near resonance condition, the 53 harmonic quadrupoles were ramped
down and the emittance measured again.  Figure 6 shows the emittance
after the machine was set back to its nominal tune. The measured values
of the emittance are 10.3 pi mm-mr and 10.2 pi mm-mr in the horizontal
and vertical, confirming the simulation results.  These preliminary
results strongly encourage us to proceed further with the "double slow
spill" scheme.
Figure 1: Initial beam profile 20 pi mm-mr emittance.
Figure 2: Beam profile during the slow spill extraction.
Figure 3: Beam profile after extraction and beam relaxation.  Beam
emittance is 18.4 pi mm-mr.
Figure 4: Beam profile before the beam tune is changed, as measured by
flying wire.
Figure 5: Beam profile with the beam very close to resonance, as
measured by flying wire.
Figure 6: Beam profile after the beam tune is changed back to normal,
as measured by flying wire.
4 The Method
Sufficiently encouraged by the simulation results and the Main Injector
data, we proceed to work out the ramp structure and cycle rates and
power consumption for various spill mixes.  Figure 7 shows the proposed
ramp structure to implement this scheme.  A single booster batch is
extracted to p-bar at points C,D, and G,H in the next ramp.  The time
interval between the points A,B and E,F is 0.141 seconds, the time it
takes the booster to input 2 booster batches at 15 Hz into the Main
Injector.  The up-ramp BC takes 0.6899 secs and the downramp DE takes
0.5856 secs.  It takes .07 sec for the extraction kicker to fire and
another .07 sec for it to reset.  It then takes 0.11 sec for the slow
spill resonance extraction system to ramp up, produce a slow spill of
1.149 seconds and another 0.11 second for the slow spill extraction to
ramp down and 0.14 seconds for the extraction kicker to fire and reset
at point D for the second proton batch for p-bar resulting in a total
flat top length of 1.649 seconds.  The time difference between the
first booster batch to p-bar and the last booster batch to p-bar, i.e.
the time difference between the points C,D and G,H is taken to be ss
1.466 seconds, the time it requires for the debuncher to be emptied.
It is the time between extractions to the p-bar under normal antiproton
production.  The time interval between D and G, the second and third
shots to p-bar is ~1.6 seconds.  We refer to this new scheme as a
"double slow spill".  So during a total cycle time of 3.066 seconds, we
deliver 2 batches to p-bar, resulting in 2349 p-bar shots per hour (as
opposed to 2455 p-bar shots per hour in the pure p-bar mode) which is a
reduction in p-bar duty factor of 4.3 % from the pure p-bar mode.  It
results in an increase in duty factor for P-907 of 648% if the double
slow spill is run every cycle as opposed to running a single slow spill
for every 10 pure p-bar cycles.
Figure 7: Proposed spill structure.
4.1 Various ramp mixes
In order to optimize duty factor versus power consumption and p-bar
production,we have run various mixes of the pure p-bar spill, single
slow spill and double slow spill.  The results are to be found in table
1.  For example, the case 1 corresponds to running 1 pure p-bar cycle,
case 2 a pure single slow spill[4] and case 3 a pure double spill.  The
cycle time for case 1 is 1.467 secs and the length of the flat top is
0.070 seconds.  The number of slow spill seconds per hour to Meson in
this mode is zero.  The average power consumption per spill is 5200
GeV2. This is the defined as
                         _ tspill
                1       |
          W = ------    |           E^2 dt
              tspill   -  0
where tspill is the time taken by the average ramp cycle and E in GeV
is the energy of the main injector ramp.  A pure single slow spill run
(case 2), which has 1350 slow spill seconds delivered per hour to Meson
but only 1350 p-bar shots per hour and has W=9233 GeV^2.  The spill
cycle time for this slow spill is 2.667 seconds, (as opposed to 3
seconds in the proposal) since we are only using two booster batches in
the spill. The Main Injector is designed to handle a power load of
~8216 GeV^2. The pure double spill case is illustrated by case 3, which
has 2349 p-bar shots per hour, 1349 slow spill seconds to Meson and a
W=9906 GeV^2, which may exceed the main injector tolerance in power
consumption.  A good compromise would be case 11, which has one pure
p-bar cycle to 1 double spill resulting in 913 flat top seconds per
hour to Meson, 2383 p-bar shots per hour and a W=8383 GeV^2 which may
be tolerable.  This case delivers 3% fewer p-bar shots per hour than
the pure p-bar case and delivers 76% of the amount of beam that we
requested in the proposal.
Table 1: Parameters for various mixes of spills
case	pure p-bar	single	double	average		average	average			slow spill	p-bar
		p-bar		slow	slow	cycle time	power	flat-top time				shots
		spills		spills	spills	(sec)		(GeV^2)	(sec)			(sec/hr)	(/hr)
 1		 1			0		0		1.467		5200	0.070			   0		2455
 2		 0			1		0		2.667		9233	1.250			1350		1350
 3		 0			0		1		3.066		9906	1.649			1349		2349
 4		 1			2		0		2.267		8363	0.857			1059		1588
 5		 1			1		0		2.067		7802	0.660			 871		1742
 6		10			5		0		1.867		7121	0.463			 643		1929
 7		10			4		0		1.809		6898	0.407			 568		1990
 8		10			2		0		1.667		6276	0.267			 360		2160
 9		10			1		0		1.576		5821	0.177			 208		2285
10		 1			0		2		2.533		8997	1.123			1089		2369
11		 1			0		1		2.266		8383	0.860			 913		2383
12		10			0		5		2.000		7605	0.596			 690		2400
13		10			0		4		1.923		7343	0.521			 614		2406
14		10			0		2		1.733		6587	0.333			 398		2423
15		10			0		1		1.612		6014	0.214			 233		2436
5 Outstanding questions
*  Is there an intensity dependence to the measurements presented here?
One should repeat them at high intensity (5E12 protons).
*  What is the minimum amount of beam that can be extracted in a
controlled fashion?
*  Is it possible for p-bar to take pulses at two dfferent time
intervals, C and D are spaced apart 1.467 seconds and D and G are
spaced apart 1.6 seconds.
*  What is the minimum spacing between pulses that p-bar can tolerate?
6 Slow Spills during MINOS running
The MINOS experiment is expected to start data-taking in late 2003.
The MINOS ramp has 6 booster batches one of which is sent to p-bar and
the other 5 to MINOS using a fast kicker.  The length of this cycle is
1.87 sec [5] which results in 1925 p-bar shots per hour, a 21.6%
reduction in p-bar stacking rate.  Running MINOS with p-bar production
results in a more severe reduction in p-bar stacking rate than anything
we are proposing using the slow spill.
If P907 is approved in November 2000, we expect to setup the experiment
in 2001 and start data-taking in 2002.  We would then have over 1.5
years to run before MINOS starts up, which is enough to acquire the
data we ask for in the proposal.  If however, we overlap with the MINOS
start-up, it is possible to devise schemes where in we have 5 booster
batches injected, one of which is given to p-bar, the remaining 4 are
used in slow spill and 3 given to MINOS and one to p-bar at the end of
the slow spill.  Another possibility is to interleave a MINOS Spill
with a double slow spill outlined above.  It would be far more
economical to have P-907 data taking be completed before MINOS turn on,
both for proton economics as well as utilizing the data for MINOS
analysis in a timely fashion.
7 Conclusions
The simulation results and the actual Main Injector behavior seem to
imply that it is possible to extract a small fraction (5-10%) of the
booster batch during a slow spill and still preserve the emittance of
the beam so that it can be used for p-bar production.  The remaining
questions have to do with the stability (regulation) of the power
supplies driving the extraction system.  Are they stable enough such
that a small steady fraction of the beam can be extracted during the
slow spill, i.e., is the current system of regulation adequate enough
to skim off 10% of the intensity in a steady uniform slow spill? Some
more development effort will be necessary to achieve the degree of
stability in the extraction system.
8 Acknowledgements
We wish to thank John Johnstone for performing the simulations.  We
wish to acknowledge useful conversations with Jim Hylen, Phil Martin
and Peter Prieto.
References
[1] Main Injector Technical Design Handbook, Chapter 2, August 1994.
[2] "P-907 Proposal to measure Particle Production in the Meson area
using Main Injector Primary and Secondary Beams", can be found at
http://wwwppd.fnal.gov/muscan/meson120/proposal/p907.ps
[3] The "double slow spill idea" was initially proposed by R.Raja to
address the duty factor crisis with P-907.
[4] This is a shortened version of the mixed slow spill given in [1]
since we only use 2 booster batches.  This cycle takes 2.667 secs as
opposed to the 3 second cycle used both in the P-907 proposal and the
design handbook.  The ramp times given in this document are approximate
and need to be made into whole number of booster "tics" appropriately.
[5] J.Hylen, Private communication.