Online longitudinal
emittance monitoring in the Main Injector for Collider operations
Author:
Kwasi
K Danquah,
Vassar
College, Poughkeepsie, New York.
Supervisors:
Chandra
Bhat, Brian Hendricks
Beams
Division,
Fermi
National Accelerator Laboratory, Batavia, Illinois
Date: June - August 2001
Abstract:
The Tevatron Collider Run II has commenced. During this run, 36 proton bunches and 36 anti-proton bunches will be loaded into the Tevatron. It is essential to monitor emittance evolution of the beams in the Main Injector before transfer to the Tevatron in real-time. This paper describes the development and features of the online console application to monitor the longitudinal emittance and intensity of beams in the Main Injector before it is transferred into the Tevatron for colliding experiments.
Introduction
The Tevatron proton-antiproton collider is
the highest energy particle collider in the world. The center of mass energy
available to study elementary particles physics is approximately 2 TeV. To
fully exploit its capability, it is very essential to understand the proton-antiproton luminosity in the Tevatron
at the CDF and D0 interaction points. Luminosity is a very strong function of
the beam emittance and as such, it is very essential to monitor and maintain
low emittance and high brightness during the acceleration.
During Run II, the longitudinal emittance
beam bunch budget is ~2eVsec at collision in the Tevatron. Thus it is very
essential that the beam emittance is less than 2eVsec before transfer from the
Main Injector into the Tevatron. This makes it necessary to monitor the
emittance throughout the acceleration process in the Main Injector for both
protons and antiprotons. Transverse emittance is also an important property
which requires attention. However, flying wire and ion profile monitor data
have shown that the transverse emittance is well maintained during acceleration
in the Main Injector.
To facilitate the monitoring of longitudinal
emittance evolution in the Main Injector, there is the SBD (Sample Bunch
Display) system. This system is capable of providing bunch by bunch data
throughout the entire acceleration. A
console program is required to utilize the data from SBD to provide information
on emittance. PA1812, designed by Guan
Wu, provides some information on the beam but does not address longitudinal
emittance and does not provide a means of storage for later retrieval and use.
Bunch specific values, which could facilitate comparisons and calculations, is
unavailable via PA1812. To solve this
problem requires a new console program that addresses all the needs for
monitoring longitudinal emittance. This program should be able to provide
emittance information throughout the entire process of acceleration and also
must be able to store data for later use.
In the Main Injector, the two potential
stages where we expect longitudinal emittance growth are transition crossing
and coalescing. During these stages, emittance is likely to be affected and
thus emphasis will be placed on monitoring data before and after these stages.
Background Information
The protons and antiprotons undergo different processes before transfer into the Tevatron for colliding experiments. The protons are initially accelerated in the Cockcroft-Walton accelerator to 750 kV, to 400 MeV in the Linac (linear accelerator), 8 GeV in the Booster, 150 GeV in the Main Injector and finally to 1 TeV in the Tevatron. On the other hand, the antiprotons start from the Recycler or from the Accumulator with kinetic energy of 8GeV. The anti-protons are then transferred in to the Main Injector to be accelerated to 150GeV and finally into the Tevatron where it is accelerated to 1TeV. During proton-antiproton colliding, protons and anti protons are accelerated in the MAIN INJECTOR separately and then later accelerated in the Tevatron.
Presently, both proton and antiprotons come in groups of four called a shot with each group containing five to seven bunches. A bunch is simply described as a group of localized particles formed due to the alternating voltage used in the RF cavities of the accelerator. The diagram below explains how bunches are formed.
Fig. 1
From Fig.1,
Consider a train of particles approaching the accelerating gap. Particle A will
reach the gap before particle B. Let the sine plot shown, represent the voltage
that exists at the accelerationg cavity in time. When particle A reaches the
gap it sees a positive voltage and it is accelerated, particle B likewise sees
a positive voltage but its values higher than A’s and so it gets a greater
kick. This allows it to catch up with A. Partices that arrive much earlier,
that is, when the voltage is negative get slowed down.
Fig. 2
Thus
trailing particles are given a greater kick and leading ones are retarded. The
resultant group of particles is called a bunch.
The stable area determined by the RF wave is known as a bucket.
Main Injector
Antiproton and Proton beams are transferred
into the Main Injector at an energy of 8 GeV.
Here, the beams are further accelerated to 150GeV. The Main Injector
uses a 53 mhz (harmonic =558) alternating voltage for which a bucket length is
about 18.87 nsec. A typical 53 Mhz bunch in the Main Injector is about 4 to5
nsec in length at 8GeV, and this decreases as the beam is accelerated to a
minimum value which is reached at transition crossing.
Presently, injected beams come four 53 Mhz groups called a shot. This consists of 21 buckets per group and 84 buckets altogether. Below in Fig. 3 is real data showing a typical antiproton shot
Fig. 3
A pbar shot consisting of 4 groups each with 7-9 bunches
After reaching 150 GeV, all bunches in each of the 4 groups are coalesced into a single bucket.
Coalescing
Coalescing is achieved by merging several buckets (usually all bunches within a group) into one bunch to increase the bunch intensity. This process is synonymous to pouring the contents of all buckets into one bucket. The next two diagrams show a group of bunches before and after coalescing
Fig. 4
A group of 7 bunches before coalescing
Fig. 5
The same group after coalescing. Only a
single bunch remains.
Thus after coalescing, a shot will consist of
four intense bunches a s shown in the next diagram.
Fig. 6
A 4-group
shot after coalescing
Transition crossing is used to prevent beams
from being lost due to relativistic effect, which occurs when the speeds of the
particles reach close to the speed of light. In a proton/anti-proton
synchrotron, transition crossing is the first potential region in the
acceleration cycle where the beam’s longitudinal emittance will grow. Emittance
tends to grow by large amounts unless special care is taken. For the Fermilab
Main Injector, the transition energy is at 20.4 GeV.
Accelerator control system
Fig 7
The accelerator control system consists of
three main components which are the front ends, centrals/servers and
consoles. Front ends are computers that
interface to various hardware in the accelerator, and this is the point where
data acquisition and hardware control take place. The centrals/servers serve as
a location for shared resources such as databases and alarm reporting.
The consoles comprise both machine and
software that provide a human interface to the accelerator. All programs that
either control accelerator operation/experiments or utilize data from the
accelerator are initiated from this component.
Sample Bunch Display (SBD)
The Sampled Bunch Display (SBD) displays the intensity, longitudinal width and RMS sigma of each bunch in the Main Injector. It consists of a Lecroy (resistive wall beam signal pick up monitor) 2.8 GHz scope and Labview data handling system. It takes raw data from the beam detectors and calculates intensity, longitudinal width and sigma values for each bunch at 25 different times in the acceleration process specified by the user. For the purposes of this program, bunch information will be read at only three points(in time), injection, flattop and extraction. This is because transition and coalescing lie in between the above mentioned points.
Longitudinal emittance:
Longitudinal emittance is a measure of how
coherent particles in a beam are. It is expressed as a function of bunch
length, RF voltage and synchrotron energy. The rf voltage and momentum will be
read from ACNET.
·
Bunch length
·
RF voltage
·
Momentum
Given the momentum, ps, synchrotron energy, Es, can be calculated using the formula:
where mp is the rest mass of a
proton/anti-proton.
Emittance Calculation:
The longitudinal emittance is calculated as
follows:
Where Vrf = rf voltage, R= radius of the accelerator, h= harmonic
number, C velocity of light, 
= relativistic gamma at
transition,
= momentum compaction factor
and Q= half bunch length expressed in radians.
Data acquisition
Data required for all calculations and graphs
is acquired from the SBD interface. The main devices that are utilized in this
program are shown in table below
|
Device
Names |
Purpose |
Structure |
|
I:SBD01I, I:SBD02I, I:SBD03I |
Intensity readings for MI
injection, MI flattop and MI Extraction |
Each device is an array of
676 elements each corresponding to a bucket. Typically the data needed is
stored in the first 84 elements. |
|
I:SBD01W, I:SBD02W, I:SBD03W |
RMS Bunch length ( 95%
width ) readings for MI injection, MI flattop and MI Extraction |
Each device is an array of
676 elements each corresponding to a bucket. Typically the data needed is
stored in the first 84 elements. |
|
I:RFSUML |
RF Voltage reading |
This device gives a single
reading |
|
I:MMNTUM |
Momentum reading |
This device gives a single
reading |
|
I:SBD01D, I:SBD02D, I:SBD03D |
Raw data values for MI
injection, MI flattop and MI Extraction. This value is a measure of amplitude
of the beam in the various buckets. |
Each device is an array of
4000 elements. The number of elements that represent a single bucket varies
with the rate at which the front ends do the readings. |
|
T:STORE |
The number used to identify data acquired from a
particular run store of the accelerator |
This device gives a single
reading. |
The program
Fig. 8
The
program consists of three main modules, namely:
Live Capture Module
This module is responsible for monitoring beams in the Main Injector. Its purpose is to repeatedly capture data on beam emittance and intensity. It only captures data at three points in the Main Injector acceleration cycle, which are:
· Main Injector Injection
· Main Injector Flattop
· Main Injector Extraction
Fig. 9
For every shot, this module goes through each
group of bunches and reads out all the relevant data on the central three
bunches. Thus, a total of 12 bunches are processed (3 from each of the 4
groups). Emittance calculations are done on the acquired data, and the results
are displayed together with intensity values in a table. This is repeated for a
total of 9 shots and then saved to disk. However, the user has the option to
save the data at any point in time.
Each time a shot enters the Main Injector,
this module is invoked and it reads all of the necessary data. The graphing
module is then invoked to plot out the current shot.
Retrieve Module
This module serves the sole purpose of displaying data previously saved by the Live Capture Module. It displays the emittance and intensity values in the same fashion as the Live Capture module. Along with these values, the user has the option to view the associated values for voltage and momentum.
Fig. 10
Graphing Module
The
graphing module plots out a graph of amplitude (Y-axis) against time (X-axis)
for all three points at which data is acquired. For every shot that is captured
by the Live Capture module, the graph module draws the graph for the shot at
Main Injector injection, Main Injector flattop and Main Injector
extraction. This module further
provides the user the capability to horizontally shift the plot by a maximum of
21 buckets and also to enlarge or shrink the plot.
Data Samples
Fig. 11
This is a snapshot
of the program after 9 antiproton shots were accelerated in the Main Injector.
The above data are values for emittance and intensity taken at Main Injector
Injection
Fig. 12
This is a
snapshot of the program after 9 antiproton shots were accelerated in the Main
injector. The above data are values for emittance and intensity taken at Main
Injector flattop
Fig. 13
This is a snapshot of the program after 9 antiproton shots
were accelerated in the Main injector. The above data are values for emittance
and intensity taken at Main Injector Extraction
Fig. 14
This is a snapshot of the graphical plot of the first antiproton shot. For this
particular shot, there are three plots representing Main Injector injection,
Main Injector flattop and Main Injetcor extraction
Fig. 15
This is a snapshot
of the plots after a range has been set from 6 to 17
Fig. 16
This is a
snapshot showing previously saved data together with values for momentum and rf
voltage
Conclusion
The longitudinal emittance monitoring console
application, PA1896 is a very important diagnostic tool used to measure the
longitudinal beam emittance during acceleration in the Main Injector. This tool
will be used as an integral part of the Tevatron proton-antiproton runs. After testing with sample pbar and proton
beam shots seems to address all the needs of an emittance monitoring system. Emittance data is captured instantly with
the option to save and retrieve later. A graphical plot of beam shots is also
provided to serve as a guide to the user and the user has an added option to
email raw data to himself/herself for further calculations. In the future a graphical plot of emittance
values could be added to the functionality to further enhance the clarity of
the information to the user.
Acknowledgements
I would
like to thank the SIST committee for giving me the opportunity to undertake
this project. Special thanks to Chandra for the accelerated physics course he
gave me during these 2 months. Thanks to Brian for helping me with the program
and teaching me all the tricks and finally Guan Wu and Wim Blokland for all the
assistance and information you provided.
Appendix
References
Martin P. S, Ohuma S. 1989. Longitudinal phase space in circular
accelerators.
Blokland W.
Overview of Main Injector sample bunch data, http://www-rfi.fnal.gov/SBDMI/SBDMI.html (July 2001)