Beam Optics (3)

Implementation of Quadrupole-Scan Emittance Measurement at Fermilab's Advanced Superconducting Test Accelerator (ASTA)

Abstract

Transverse emittance measurements based on the quadrupole scan technique have been widely used to characterize the beam phase space parameters in linear accelerators. This paper discusses the implementation of the technique at the Advanced Superconducting Test Accelerator (ASTA) at Fermilab. We plan on deploying a flexible implementation that permits an operator to select a quadrupole with associated analyzing screen to measure the beam emittance. Our implementation utilizes Python scripts combined with Fermilab’s control system ACNet and ELEGANT tracking code. We also discuss the applicability of the quadrupole scan method at at an operating charge of at ASTA. Some preliminary measurements will also be presented.

Introduction

The Advanced Superconducting Test Accelerator (ASTA) has been constructed and commissioned in Fermilab and it is currently scheduled to build a high energy beamline (150 – 300 MeV) by adding a cryomodule with construction plan of the Integrable Optics Test Accelerator (IOTA) ring by 2016. Most recently, 20 MeV of electron beam energy was successfully demonstrated in the ASTA injector beamline and it is planned to increase the beam energy up to 50 MeV with the schedule to add a capture cavity downstream of the photoinjector. Along with the timeline of the construction/commissioning schedules, it is necessary to assure a beam monitoring technique for a full scale transverse and longitudinal phase-space characterization of a commissioned beam, which enables to precisely operate the machine. Instantaneous monitoring of beam parameters is highly required for preserving the beam emittance along the beamline. We have been working on the idea of developing a real-time emittance monitoring system based on a quadruple-scan technique [1][4]. Our plan is to design a Python script programmed with a quad-scan algorithm and to implement it in the ASTA beamline control system (ACNet console). We expect that successful development of a designed system will allow a beamline operator to trace temporal profiles of transverse beam parameters and also to systematically control the dynamics using quadrupoles installed in the ASTA beamline.

beam dynamics

Emittance is an important property of charged particle beams, allowing for a description of beam quality and the comparison of beams. Generally, emittance can be described in six-dimensional phase space as the spread of density of particles in the beam. In many cases, the transverse emittance is of particular interest and the six-dimensional phase space is split into subspaces comprised of and [1].

The area occupied by the particles of interest may be considered as being bound by an ellipse and can mathematically be described by the following beam matrix:

(1)

Equations from Paper

Figure 1: Beam ellipse with physical interpretation of the physical components

Using the beam matrix, the geometrical emittance can then be defined as:

(2)

The beam ellipse and matrix can also be expressed in terms of the Courant-Snyder parameters:

(3)

, where, and [2].

A more complete description of the emittance may given as the root mean square emittance. With this description, the moments of the particle distribution in phase space can be related to the beam matrix elements by [1]:

(4)

This new description of the beam matrix now gives a more relatable physical meaning: is the square of the rms beam size, is the square of the divergence, and are the cross-correlational terms. With this useful new description, a normalized is now described by:

(5)

where this time and are the relativistic factors [3].

Quadrupole Scan

The quadrupole scan technique (quad scan) is a simple and widely used method for measuring transverse emittance at a particle accelerator. The goal is to measure the beam size of the particle beam as a function of the magnetic field strength of a quadrupole magnet at some imaging station (typically an OTR or YAG screen). This information allows for the determination of, the Courant-Snyder parameters, and the emittance. One way to approach the quad scan technique is to use a thin lens approximation [4]. This method views the quadrupole magnet as a thin focusing (or defocusing) lens and then utilizes transfer matrices. If represents the transfer matrix of the quadrupole and represents the transfer matrix between the quad and the imaging screen (where is the drift length and is the quad field strength multiplied by the quad length), then the transfer matrices may be written as:

, which is used to find the beam matrix:

A quadrupole of choice is selected along with an imaging station and the field strength is varied (finding the minimum spot size is needed before evaluating the range of the scan in the field strength). Plotting the beam size (squared) as a function of and applying a parabolic fitting function which yields three coefficients:

which can then be equated to the beam transfer matrix:

which upon solving gives the beam matrix elements:

The transverse emittance is then found via the square root of the determinant of, as stated in the section above. Courant-Snyder parameters can found using these coefficients or by simply using the three C-S equations mentioned in the previous section [4].

PRELIMINARY RESULTS

It should be noted that the following preliminary results were obtained using the thin lens approximation and that much work and analysis is currently taking place.

Figure 2: Beam size as a function of quadrupole field strengh in the horizontal plane at ASTA using quadrupole Q112 on a YAG imaging screen at the imaging station X120

Table 1: Beam parameters from quadrupole scan with the Q112 quad at the X120 imaging screen

prospective tests and activities

Figure 3: Schematics of ASTA injector beamline

Since March 2015 the Advanced Superconducting Test Accelerator (ASTA) at Fermi National Laboratory in Batavia, IL has been operating with a electron beam (with future plans to reach energies up to).

The long-term goals of this project are:

Program a Python script of the quad-scan transport matrices based on the “Thin Lens Approximation” and “Thick Lens Model”.
Design script with imported raw data (such as magnetic field data from an ASTA quadrupole magnet).
Test and prove the script with ASTA beam parameters.
Simulate a quad scan of an existing ASTA beamline component with ELEGANT simulation.
Benchmark the ELEGANT simulation with the analytic model programmed in the Python script.
Develop a networking platform of the Python script with the ACNet console at ASTA.
Apply the generic Python code into the ACnet console, allowing an operator to select any quad or screen that they would like to use, allowing for automatic feedback and measurement of the beam size and transverse emittance.

CONCLUSION

Emittance from charged particle beams is integral in describing certain beam characteristics as well as being a useful tool to compare the quality of beams. The quadrupole scan technique is a simple and useful method for measuring the transverse emittance of a beam and the goal of this project is to implement this method using Python script and ELEGANT simulation with the ACnet console at the ASTA facility at Fermilab. This will allow an operator to readily choose a quadrupole magnet of interest and measure the beam size and emittance at an imaging station of choice.

acknowledgment

I would like to thank D. Broemmelsiek , D. Crawford, D. Edstrom, P. Piot, J. Ruan, G. Stancari, and A. Valishev of Fermi National Accelerator Lab (FNAL) for the technical support for quad-scan tests of the Advanced Superconducting Test Accelerator (ASTA).

Beam Dynamics

Quad-Scan

Quad-Scan

Preliminary results (a) Python (b) Elegant

Summary/Plan

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