Calibration Of Proton Accelerator Beam Energy

TL;DR

This paper presents a method to calibrate proton beam energy in RF accelerators by using reaction thresholds and simulations to accurately determine energy distribution, improving precision in nuclear reaction studies.

Contribution

A novel calibration technique that uses reaction data and simulations to accurately determine proton beam energy and distribution in RF accelerators.

Findings

The method accurately estimates beam energy using reaction thresholds.

Simulation data confirms the linear relationship in energy distribution.

The approach is validated against experimental data with satisfactory results.

Abstract

When studying the 7Li(p,n)7Be reaction with a RF accelerator, it is difficult to define the precise energy of the beam and its energy distribution, which together fully define the beam, for our purpose. What we do know is the difference between two given energies. We resolve this problem by finding a reference energy and then finding another energy by examining the data, relative to the reference energy. From the difference between them we can approximate the energy distribution for a given energy, and since we know the energy threshold of the reaction (E_threshold for 7Li(p,n)7Be is about 1880.4-1880.8 (keV)) we can calibrate the beam energy. We then determine the energy which produce the maximum yield derivative as the reference and record the energy whose neutron yield is 5% of the reference energy. The data is collected by simulating this reaction using SimLit. Since this is a simulation we know the real energy distribution so we make a linear fit for energy distribution as function of energy difference. We tested the theory on experimental data for which we approximate the energy distribution by other means, and found our new method to be accurate and satisfactory for our needs.

Tables

Table 1. Table 1: The data from SimLiT simulation at 5 degrees. Energy’s value presented in keV. The data ploted on figs ( 5 ),( 6 ).

index	energy sigma	low energy	reference energy	energy difference
1	1	1876.2	1884.4	8.2
2	2	1875.8	1884.4	8.6
3	3	1875	1885	10
4	4	1874	1885.6	11.6
5	5	1872.8	1886.4	13.6
6	6	1871.6	1887.2	15.6
7	7	1870	1887.8	17.8
8	8	1868.6	1888.6	20
9	9	1867	1889.2	22.2
10	10	1865.6	1890.2	24.6
11	11	1863.8	1890.4	26.6
12	12	1862	1891	28.6
13	13	1861	1891.8	30.8
14	14	1859.2	1892	32.8
15	15	1858	1894	36
16	16	1856	1893	37
17	17	1854.4	1894	39.6
18	18	1853	1894.6	41.6
19	19	1851.4	1895.2	43.8
20	20	1849.8	1895.6	45.8

Table 2. Table 2: The data from SimLiT simulation at 15 degrees. Energy’s value presented in keV. The data ploted on figs ( 5 ),( 6 ).

index	energy sigma	low energy	reference energy	energy difference
1	1	1877.2	1886	8.8
2	2	1876.8	1886.2	9.4
3	3	1876.2	1886.8	10.6
4	4	1875.2	1887.4	12.2
5	5	1874	1888	14
6	6	1872.6	1888.6	16
7	7	1871.2	1889.4	18.2
8	8	1869.8	1890	20.2
9	9	1868.2	1890.8	22.6
10	10	1866.8	1891.2	24.4
11	11	1865.2	1891.6	26.4
12	12	1863.6	1892	28.4
13	13	1862	1892.8	30.8
14	14	1860.6	1893.4	32.8
15	15	1858.8	1893.6	34.8
16	16	1857.2	1894.2	37
17	17	1855.6	1894.6	39
18	18	1854.2	1895.4	41.2
19	19	1852.6	1896.2	43.6
20	20	1851	1896.6	45.6

Table 3. Table 3: The data from the real experiment,which extracted by the same means as at the simulations. Energy’s value presented in keV

index	energy sigma	low energy	reference energy	energy difference	energy sigma*	reference energy value*
1	1.5	1871	1873.6	2.6	-0.1	1882.1
2	15	2015	2070.4	55.4	24.37	1899
3	20	2020	2073.2	53.2	23.35	1898

Equations

$$\sigma (△E)=0.463\bullet △E-1.3$$

$$E_{reference}(△E)=0.289\bullet △E+1883$$

$$\sigma (△E=2.6(keV))=0.463\bullet 2.6-1.3=-0.096(keV)$$

$$E_{reference}(△E=2.6(keV))=0.289\bullet 2.6+1883=1883.4(keV)$$

$$\sigma (△E=55.4(keV))=0.463\bullet 55.4-1.3=24.37(keV)$$

$$E_{reference}(△E=55.4(keV))=0.289\bullet 55.4+1883=1898.7(keV)$$

$$\sigma (△E=53.2(keV))=0.463\bullet 53.2-1.3=23.35(keV)$$

$$E_{reference}(△E=53.2(keV))=0.289\bullet 53.2+1883=1898.1(keV)$$

Full text

Racah Institute of Physics, The Hebrew University, Jerusalem, Israel, 91904

1 introduction

Our research uses a RF proton accelerator to produce ${}^{7}Li\left(p,n\right)^{7}Be$, and it is crucial to define the beam energy as accurately as we can. To do so we need the exact energy value and the energy spread (standard deviation), that from now on will be referred to as “energy sigma”. Although we don’t know the two values mentioned above, we do know the gap between any two energies the accelerator produces. Moreover, we can measure the number of neutron yield for a given angle with a Long Counter Detector. To solve our problem, we search for a well defined energy as a reference. By extracting this energy we can find another energy that conserves some relation value which we explain later on. After collecting these differences and their energy sigma we assume they fit each other linearly. Moreover we assume that the energy differences can point out the real value of the reference energy again by linear fit. This method is a new way to calibrate the proton beam energy. By putting in the equations the measured value of the energy difference extracted from a given experimental data, we can get the energy sigma and the real value of the reference energy (“new reference energy”). The rest is calibrated in reference to the new reference energy, since as we mentioned before we do know the gap between any two given energies. We tested this method and confirmed it on experimental data. Furthermore, we found that the angle contributions111Meaning we made the fit of energy sigma and reference energy value vs. energy difference for different angles and the fits were almost the same. for this method in a Long Counter Detector are negligible.

2 methods

2.1 simulation with LiLiT

First we did simulation with SimLit at wide spectrum in terms of energies, angles222The angle between the direction of the proton beam to the scattered neutron., and energy sigma. Of ${}^{7}Li\left(p,n\right)^{7}Be$ reaction caused by accelerate protons on lithium target. The simulation sets we did where to take a constant energy spread and constant maximum angle, meaning we count all neutrons who scattered from the center of the target up to the maximum angle we determine. And we let the simulation to run on a rang of energies far less then the reaction threshold and up to 2 MeV. The simulation based on “Monte Carlo” that rely on repeated random sampling to compute their results. Verifying we make at least 10,000 events compensate the statistical error which is square rout of the samples number and to be as accurate as 1%. The data we extract were the excitation function and they look like figs (1) and (2).

2.2 analysis of computed data

To find a uniquely defined energy in the excitation function (shown in fig (1)) we take the derivative of the this function333The excitation function as bean smooth by interpolation fit and putting many extra energies. The derivative as bean fitted to an superposition of two gaussian to avoid noise. (shown in fig (1)) and as can be seen we found a very distinct peak of yield density 444yield density is define to be the derivative of the yield vs. energy function.. We chose the energy that fits this peak as our reference energy. We define the lower energy as the energy which produces around 5% of the reference energy neutron yield. This act prevents noise interference. After doing so for several simulations we extract the values of the difference between the two energies in each experiment, and we know the energy sigma and the real value of the reference energy because this was a simulation. We did this analysis for different sets with the same statistics per cross section. From this data we extract a linear fit of energy sigma as a function of the gap, fig (5). And a linear fit of reference energy value as a function of the gap, fig (6).

2.3 the data from the simulation

Here is the function that we extracted :

[TABLE]

[TABLE]

And this is plot of the data with their fit.

2.4 using those fits to calibrate experimental data

Assuming this phenomena is an continues phenomena. We can imagine that if we do the same analysis on a real experimental data, who done approximately at the same conditions. We will get a value for the gap between the high energy and the low one. Now instead of making a set of points we gust put the energy gap in the fit we gust mentioned, and extract the energy spread an the real absolute value of the reference energy. This method doesn’t take in to account any physical dimensions of the problem, and it doesn’t use any absolute value of the problem but the peak at the derivative function which is a characteristic of the problem.

3 results

Our results as we extracted from the data by these means are shown here, we present three different data sets, that we estimated the energy sigma and the shift of the energy axis, using our new method and other methods555TRIM calculation and Geant4 simulation for cooperation.

First data set we approximate sigma to be 1.5keV while the new method shows.

[TABLE]

[TABLE]

Second data set our approximation sigma is 15keV while the new method shows.

[TABLE]

[TABLE]

Third data set our approximation sigma is 20keV and shift of keV while the new method shows.

[TABLE]

[TABLE]

all the data as we extract can be seen at table (3).

4 summary

As we said this method doesn’t take in to account any physical dimensions of the problem. Which make it an independent new way to analysis of the experimental data.

To use this method do the following:

• •

Fit your data as good as you can.

• •

Derive this fit and find the energy that gives the maximum.

• •

Find the neutron yield at that energy.

• •

Find the energy at which you measured 5% yield.

• •

Subtract one from the other and take the absolute value; this value is $\vartriangle E$.

• •

To find your approximate energy distribution use equation (1) as shown in equations (3) and (5).

• •

Change the energy value of the high energy according to equation (2) and change the axis values with the same scale as before, now using the new energy as reference point.

VERY IMPORTANT - make sure the low energy yield value is more than 5% !!! else you need to extract the fits for the sigma energy and the real value of reference energy, referring to the minimum present you can get from the specific data. our fits is relevant for long counter detector and thick lithium target.