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Abstract- Medical Linear Accelerators (LINAC) are heart of Cancer treatment machine. The inside of the accelerator guide consist of a series of microwave cavities, which are shaped to high accuracy to keep the radar-like wave in synchronism with the accelerating electrons, and which are coupled together to feed microwave power along the accelerator guide. The shunt impedance of an RF accelerator determines how effectively the accelerator can convert supplied RF power to accelerating gradient. The shunt impedance is figure of merit of a medical LINAC. This paper discussed automated system to calculate Shunt Impedance of LINAC using Slater perturbation Theorem. Virtual instrumentation (VI)Â is the use of customizable software and modular measurement hardware to create user-defined measurement systems,Â called virtual instruments. The developed system uses stepper motor with NI Universal Motion Interface (UMI)-7774 to position bead inside the cavity using Kevlar thread. E series network analyzer (Agilent ENA E5071C) is used to measure the resulting frequency shifts.ENA and stepper motor are controlled by NI NI PXI-8104 Embedded Controller using LABVIEW 8.6 software. Longitudinal motion of bead is used to measure shunt impedance. Program (Virtual Instrument) using LabVIEW is developed to acquire readings from network analyzer and to control motion of stepper motor. Readings are obtained for Teflon bead and Copper bead using this VI. A comprehensive analysis of the experimental results is presented. This setup reduces the drawbacks of manual bead puller setup.
Keywords - ENA, PXI (PCI extensions for Instrumentation), Shunt Impedance, UMI, VI.
Medical electron linear accelerators (LINAC) are used in cancer treatment machine. In this LINAC has the roll of accelerating electrons inside it. LINAC is made of microwave cavities which are combined with washer like disks to form a hollow copper pipe. Resonant frequencies, Q-value, shunt impedance are important parameters of LINAC which are called figure of merit of LINAC, out of these shunt impedance calculation is most critical and time consuming job.
(1) The intense electric fields, which accelerate electrons along the cavity axes, are set up by electric currents flowing on the inner cavity surface. Power dissipated in the copper inner surface of a traveling wave or a standing wave gradient accelerator guide is as follows:
P=V2/ZL Z=Shunt impedance per unit length. V= Voltage
L=Length of the accelerator. V=voltage
The shunt impedance measures the efficiency of the accelerator. Higher shunt impedance means higher electron energy gain for a given microwave power.  Thus, to minimize cost one seeks an accelerating structure with large shunt impedance.
For calculating shunt impedance, Slater perturbation theory is used. According to Slater perturbation theory, the change in resonant frequency upon introducing an object into the cavity field is proportional to the relative change in stored energy. LabVIEW software is used to calculate shunt impedance of LINAC. LabVIEW is a commercial high level graphical programming language that is designed for data acquisition and control. The graphical approach provides an intuitive understanding for how the program is structured and offer-s far greater flexibility for alteration.  Programs generated by LabVIEW is called virtual instrumentation (VI). Every VI consists of two windows: the first is called the block diagram which is where the code is held and edited and the second is termed the front panel which is the interface with the user.
SHUNT IMPEDANCE CALCULATION
The shunt impedance of a resonant type accelerating
structure is calculated using perturbation techniques. This
technique is based on slater perturbation theorem given
by Eq.1. The change in the frequency of a microwave cavity depends on the volume, shape, material and position of the perturbing object. If the perturbing object is small, then the change in frequency Ï‰ is very near to the unperturbed frequency Ï‰0. Therefore stored energy can be written as
(2)Where, , U is stored energy, H and E are magnetic field and electric field, Î¼ is permeability, Îµ is permittivity and k is a constant depending on the volume Î”Ï„ï€ of the perturbing object. If H=0 then the above equation reduces to a simple form given by Eq.2.
The quantity E2 /U can be determined experimentally
by placing a perturbing object of volume âˆ†Ï„ into the cavity and measuring the resultant frequency. If the electric filed is constant then
Therefore, r/Q can be written as
For standard cylindrical cavity operated in TM010 mode, the constant kÎµÎ”Ï„ï€ hence forth called as form factor determined for a perturbing bead. The ratio r/Q for a cylindrical cavity in TM010 mode is given by 371L/D where L and D are length and diameter respectively , .
A. Drawbacks of manual bead pull measurement setup
Manual bead pull measurement setup to calculate Shunt impedance is as shown in Fig 2.1
It is not possible to move the scale exactly 1mm distance each time for Bead-pull test as shown in Fig 2.1 (many times the slider moved 1.1mm or 0.9 mm.).
For a 30 cm long LINAC 300 Readings are taken so chances of errors are high.
The force, with which Scale is pulled down, causes backlash error, which disturbs the reading. So accurate torque must be supplied to the system
Figure 2.1-Shunt Impedance Measurement setup
Above mentioned drawbacks can be reduced by implementing automated bead puller system for measurement of cavity parameters of LINAC.
AUTOMATED SYSTEM HARDWARE DESCRIPTION
The measurement system consists of four instruments, each controlled by a computer via a GPIB interface using the data acquisition software LabVIEW and LINAC. The perturbing object (or bead) is suspended on a Kevlar thread and is drawn through the centre of the cavity using a stepper motor controlled linear drive via a mechanical assembly consists of pulleys. Figure 3.1 shows automated setup for shunt impedance calculation.
PXI: A PCI extension for Instrumentation (PXI) is a rugged PC-based platform that offers a high-performance, low-cost deployment solution for measurement and automation systems. PXI also adds mechanical, electrical, and software features that define complete systems for test and measurement, data acquisition, and manufacturing applications. PXI systems are comprised of three basic components chassis, system controller, and peripheral modules . NI PXI 8104 Embedded controller, NI-PXI-7340 peripheral module Motion I/O part are used.
Figure 3.1 Block diagram of the bead-pull set-up.
Motor: The UMI-7774(Universal Motion Interface) is standalone connectivity accessories designed to be used with National Instruments 73xx series motion controllers for up to four axes of simultaneous or independent control. One axis of it has been used. UMI-7774  connects third-party stepper and servo drives (amplifiers) and/or feedback and digital I/O to National Instruments motion controllers (Figure-3.2). DMX-R-DVR-17 motor of Arcus Technology is used. This motor is connected to back side at the base of mechanical assembly.
Figure3.2- NI Motion-7340 interfacing with NI UMI-7774, UMI is connected with third party driver unit and motor
ENA: Agilent E series Network Analyzer is used. E5071C operated at 9 KHz-4.5GHz. ENA have measurement delay 41 msec. Fig 3.3 shows front panel of ENA, Fig 3.4 shows rear view of ENA. NI provides many VIs to control E5071C from PC.
Figure3.3 Front Panel: Names and Functions of Parts
Figure3.4 E5071C Rear View
GPIB: General purpose interface bus is use to get data from ENA.GPIB HP82357 is use. GPIB cable is connected to ENA at one side and to PXI 8104 through USB.
The coordination between the motion and data acquisition is tricky. There are two methods of dealing with it: one is to probe the position of the perturbing object and measure the frequency of the network analyzer in a certain time gap, while the motor is running with a constant speed; the other way is to stop the motor while the computer is acquiring data. First one is developed and explained in this paper.
AUTOMATED SYSTEM SOFTWARE
Software used for data acquisition and analysis is Labview. Application software is divided into three main categories - configuration, prototype, and application development environment (ADE).To configure the system, National Instruments offer Measurement and Automation Explorer  an interactive tool for configuring motion control, and all other National Instruments hardware. For motion control, Measurement and Automation Explorer offers interactive testing and tuning panels that helps to verify system functionality. National Instruments offers a tool called NI Motion Assistant. NI Motion Assistant  is an interactive tool with which motion parameters can be configured and generate LabVIEW code based on requirement.
For getting access to ENA through PXI(PC) NI provides agena VIs, among these agenamarkerdata.vi is used to read response value of selected marker. Code generated by NI Motion Assistant and agenamarkerdata.vi is combined and synchronize to make complete automated system.
Using NI Motion Assistant or Measurement & Automation Explorer it is found out that for 50 steps input ('position' is one of the control of VI) bead will move 1 mm distance. Proper working of system totally depends upon controls of VI. Fig 4.1 shows block diagram of main VI and Figure 4.3 shows front panel of main VI.
Figure 4.1Block Diagram of main VI
Figure 4.2 shows the hierarchy of main VI. This hierarchy shows the sub VI's contains in main VI.
Figure 4.2 main VI hierarchy
MARKER SUB VI takes marker reading from ENA, find outs square root of delta f, write readings to spread sheet file, delta f , square root of delta f to spreadsheet file, both delta f and square root of delta f verses distance plotted on XY graph.
AREA UNDER THE CURVE SUB VI CALCULATES number of cavities present in LINAC, start and end of each cavity and area under the curve (Graph of delta f verses distance) for each cavity.
SHUNT IMPEDANCE CAL VI calculates shunt impedance of LINAC using above calculated parameters.
Figure 4.3Front Panel of main VI
Input parameters in LabVIEW are called controls which can be changed by user. Some of the controls description as follows.
Length (cm): Length of LINAC is measured and it is used in program for further calculation.
Direction to take readings: As longitudinal motion of bead is used to take readings so there are two cases to take readings.
0= For taking Readings from top to bottom.
1= For taking reading from bottom to top.
If other than 0 or 1is input for this control then Default case is executed i.e. program for case 0 is executed.
Velocity: Velocity can take any positive value. Target or maximum velocity is in steps/second (stepper axes) or revolutions per minute. Unit of velocity is steps per second.
S Curve Time: S-curve acceleration and deceleration refers to the shape of the velocity profile of a given move. Without using s-curve acceleration when an acceleration, velocity, and position, are loaded in program, the motor tries to go from 0 to the specified acceleration instantaneously. When a motor does this, it creates a trapezoidal velocity profile. When the motor is ready to stop, it once again goes from 0 acceleration to a negative acceleration as fast as it can until it is at 0 velocity and then abruptly stops. These abrupt starts and stops create the sharp corners of the trapezoidal profile. The sharp corners translate to a very high jerk. Jerk is the derivative of acceleration and refers to abrupt changes in acceleration. The s-curve is used to slowly reach a certain acceleration or deceleration.
ACCELERATION & DECELERATION: Accelerations means how fast the system achieves given velocity and deceleration means how fast system velocity goes to zero. It has minimum value of 4000 steps/sec2 .Acceleration and deceleration are typically limited to avoid excessive stress on the motor, mechanical system, and/or load.
Capture Time (msec): It is the time to capture readings from ENA. In Labview for getting marker reading from Agilent ENA VI is available, (agena markerdata.vi), which is modified to get continuous reading throughout the bead motion in LINAC. This markerdata.vi is useful to take selected marker and channel readings from network analyzer. Use of 'For loop' is done and delay is added inside the 'For loop'. Control for delay is in milliseconds. Depending on no of readings For loop is executed and agenamarkerdata.vi will take readings from network analyzer and it will be stored in spreadsheet file.
For Shunt impedance calculation area under the curve is to be found out. Curve is drawn using delta f and corresponding distance traveled by bead. To calculate this area numeric integration VI is used. It performs numeric integration on the Input Array using one of four popular numeric integration methods. Symbol for numeric integration VI is as shown in Fig 4.4..
Figure 4.4Numeric integration VI
1. Trapezoidal Rule (default)
2. Simpson's Rule
3. Simpson's 3/8 Rule
4. Bode Rule
Each of the methods depends on the sampling interval (dt) and computes the integral using successive applications of a basic formula in order to perform partial evaluations, which depend on some number of adjacent points. The number of points used in each partial evaluation represents the order of the method. The result is the summation of these successive partial evaluations.
where j is a range dependent on the number of points and the method of integration.
An indicator in LabVIEW indicates output of any VI. Required output can be displayed on front panel using indicators. Some of the indicators explain bellow.
TOTAL TIME REQUIRED FOR TAKING READINGS: This indicator indicates total time required to take readings for calculating shunt impedance. This is the time required to take readings in one way. It is calculated as follow
Time totally depends on length of LINAC and velocity with which bead will move, there will be milliseconds of delay between two readings. Unit of time is Sec.
NUMBER OF READINGS: For proper synchronization between bead motion and network analyzer data taking, number of readings must be properly calculated. By using user input parameters, number of readings is calculated in block diagram and displayed on front panel.
No of readings= position/ (velocity * Capture time).
Velocity and capture time is entered by user which are used as it is while position is calculated as follows.
Max frequency (f0): This indicator shows the resonant frequency of LINAC.
Cell No: Cell NO indicator indicates number of cavities present in a LINAC.
Shunt Impedance: Shunt impedance indicator shows shunt impedance of LINAC in Mâ„¦.
Two graph indicators are also present. One graph indicates graph of Delta f verses Distance while other indicates âˆšâˆ†f verses Distance.
Distance Traveled by bead between two readings (cm): This indicator indicates distance traveled by the bead in capture time. When one reading is taken from ENA bead will displaced the distance equivalent to this indicator. Internally in Block Diagram it is calculated and displayed on Front Panel.
Different shapes and sizes of beads are used to analyze the automated system. Different options available for beads are metallic beads or dielectric beads. Perturbation in frequency is more for metallic bead compared to dielectric bead so metallic is not preferable. We are using Teflon bead and one metallic bead. 6 MeV LINAC of 30 cm length is used to take readings by varying controls on front panel. This LINAC has resonant frequency of 2.995 GHZ.
Following readings are for Teflon bead having length of 1cm and 3mm diameter.
Table 1.Teflon bead results
D=Distance traveled by bead within two readings
S=S curve time L=length of LINAC
N= No of readings
T=Total time required to take readings
From above reading we observe that mechanical system will work properly for third and fourth set of readings. It is observed that for velocity 50steps/sec and S curve time 10 similar readings are obtained when velocity is 5 steps/sec and S curve time as 8. Figure 5.1 shows the Graph of verses distance for fourth set of readings. LINAC consists of first two buncher cavities, next 4 full main cavities and last one half cavity. Shunt impedance per unit length obtained by calculation is 107.39Mâ„¦.
Figure 5.1 Graph of verses distance for Teflon bead
Similarly results for metal bead of 4mm length and 4.75mm diameter are obtained. Metal bead is made of copper. Shunt impedance obtained per unit length by calculation is 78Mâ„¦.
Acceleration and Deceleration is kept constant 6000step/sce2
Table 2. Metal bead results
Fig 5.2 shows the graph of verses distance for 50steps/sec Velocity and S curve time 10. Total time required is 5.33mins.
Figure 5.2 Graph of verses distance for Metal bead
Using Slater perturbation theory and developed automated bead puller system, shunt impedance of 6 MeV LINAC is obtained as 107.39Mâ„¦ by Teflon bead and 78 Mâ„¦ by metal bead. Both beads used are of large size (Teflon bead length=1cm, Metal bead length= 4.75mm). Metal bead affects both electric and magnetic field which is not required, Dielectric material affects only electric field which is expected. Original shunt impedance per unit length for 6MeV LINAC is 98 Mâ„¦. Result obtained by Teflon bead is good compare to metal bead. Automated bead puller system overcomes many disadvantages of manual bead puller system. This automated system reduced time to take readings of perturbed frequency. Accurate readings are possible. As bead is in continuous motion jerk problem of manual bead puller method is removed. Man power required is reduced. It is observed that LABVIEW is best software for data acquisition and analysis.