Generation of energetic particles in accelerators
| The science and technology of radiation detection has occupied a significant portion of modern science and technology because of its great impact in numerous applications in various fields such as information of material down to parts per million, study of astrophysical objects, archaeology and geology, biophysical imaging with high sensitivity. |
| There are three major criteria behind the design of a good nuclear detector, i.e. (i) choosing an appropriate material as detection medium primarily based on ion –mater interaction, (ii) conversion of incident energy in reliable electrical signal and (iii) design an appropriate electronic circuit to process this electrical signal with minimum noise. |
| It is also important to know how the energy of the particles is enhanced before they interact with the detection medium. Nature obviously provides energy to different particles by several processes. For example, photons generated in atomic transition have typical energies in the range of electron volt (eV), X-ray photons have energy in the range of kilo electron volt (keV) and gamma ray photons have energy in the range of mega electron volt (MeV). Particles coming from cosmic ray shower have a range of energies. It is also possible to use artificial means to enhance the energy of the particles. Therefore, a natural question arises: |
| How to increase energy of the particles? |
| Highly energetic particles can be generated by a man made machines, known as particle accelerators. Here we will discuss basic principles of some of these particles accelerators. Historically, the credit of design and use the first modern accelerators goes to Cockroft and Walton, who in 1932 demonstrated the generation of 400 keV protons followed by the first ever artificial nuclear disintegration- that of lithium nucleus by means of these protons for the first time. The basic principle of operation of this accelerator was to charge a large number of condensers connected in parallel and discharge in series when the voltage across them becomes equal to the sum of the voltages of the individual condensers. Almost at the same time, an electrostatic accelerator was designed by Van de Graff, popularly known as Van de Graff generator. In this generator, a charge Q is transported to a huge condenser C, resulting in a high voltage, V = Q/C, which is used to accelerate the ions generated in an ion source. Fig.m2. 1 shows the basic features of this generator. A high voltage is used to spray positive charges on an insulating belt, which is driven by a motor to carry the charges continuously to a dome shaped terminal, where they are removed. Positive ions, like protons, deuterons, alpha particles etc. are produced in ion source and accelerated in the evacuated accelerating tube and gains energy qV, if it attains a charge state q. Eventually they are accelerated in the evacuated accelerating tube. Energy of the order of few tens of MeV can be generated in this machine. |
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FIGURE m2.1: Schematic diagram of a Van de Graff generator |
| In order to enhance the energy a Tandem Van de Graff accelerator is designed, where two insulating columns are used one after another (in tandem) , in one tank so that the particles gain an energy twice that of Van de Graff generator. There are two types namely namely, (i) folded type and (ii) straight line type tandem used for acceleration purpose.. During same time, a concept of a linear resonant accelerator, popularly known as linear accelerator or linac was suggested and later on various heavy ion linacs were designed and constructed. The first successful linac was developed by Louis Alveraz and co workers, after World War II, which successfully energised protons upto 32 MeV. The basic principle of linac is that it accelerates particles in a straight line by means of an oscillating (radiofrequency) electric field, which provides a series of boosting kicks in correct phase at a series of electrode gaps (Fig. m2.2). The emergent beam from linac is highly collimated with high intensity. |
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FIGURE m2.2: Schematic diagram of a Van de Graff generator |
| The ions get accelerated only in the gaps between two tubes where they are acted upon by the electric field present between the tubes , but travel with constant velocities in the field free space inside the drift tubes. Suppose the ion source S, some positive ions are generated in the ion source S . First these positive ions pass through the cylinder S1 to the gap 1 between S1 and S2. If q be the charge of each ion, the increment in their energy due to potential V is qV. Now again within S2 the ions move with constant speed and come to the next gap between S2 and S3 and get accelerated in the gap provided they arrive in the gap when S2 is positive w.r.to S3. In this way the acceleration process goes on with the alternate tubes connect electrically. Suppose the distance between the two gaps is l, and v be the velocity of the ion then, |
l/v = T/2 = 1/2f ——- (m2.1) |
| where T is the time period and f is the frequency of the oscillator. Length of the successive tubes keeps increasing to be in phase for acceleration. Length of tube and RF field is adjusted in such that ion ion exiting a tube sees 1800 phase change in RF field with respect to its point of entry. |
| Energy gained by the ions due to n accelerations in n gaps would be, |
E = nqv = 1/2 Mv2 —— (m2.2) |
| These expressions get modified due to relativistic correction* when the particle energy becomes quite high. Both Van de Graff generator and linac are electrostatic accelerators. Now we will discuss about an electromagnetic accelerator having circular geometry and popularly known as cyclotron. Cyclotron was first devised by Lawrence and Livingstone of University of California at Barkeley. This accelerator basically consists of two flat semi circular hollow metal boxes known as dees (D) (because of their shape) having diametric edges parallel and slightly separated from each other. They are connected to a radio frequency oscillator, which essentially generates a high frequency (10 6 Hz) alternating potential between the dees, which act as electrodes. The dee structure is placed between the poles of a large electromagnet. An ion source is kept at the centre between the dees. Considering it generates protons , the mechanism of acceleration is explained based on Fig. m2.3: |
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FIGURE m2.3: Schematic diagram of cyclotron |
| when D1 is negative, protons being positively charged are attracted towards it. Inside D1 the protons make a circular path say of radius R due to magnetic field. If the magnetic field strength is B, and the velocity of proton is v, then the radius R can be determined from the formula |
m pv 2/R = Bev —— (m2.3) |
| where m p and e are the mass and charge of a proton respectively. Inside the dee the protons are in a electric field free zone and therefore moves with a constant velocity. After travelling one complete semicircular path it comes at the edge of D1. If now the potential in the dees is adjusted in such a way that D2 becomes negative and D1 is positive , the proton will be attracted towards D2, accelerated and gaining further speed will enter inside D2. In a similar manner it will make a semicircular path inside D2 and come out at the edge of D2, where if the direction of field is changed will gain further energy and will enter insideD1. This process will continue and the proton will gain very high energy through several rotations. When it comes near the circumference of the dees, an electric field can be applied to extract the proton beam out and to focus it to the target. Now the maximum kinetic energy of the particle coming out of the machine can be calculated from the following formula: |
(K. E.)max = ½ mp vm2 = ½ (Rm eB/m p)2 = e2 B2 R m2 /2m p —— (m2.4) |
| Cyclotron can energise charged particles to several MeVs, however, it suffers from a limitation due relativistic enhancement of mass which eventually start slowing down the particle. I am not going to discuss this matter in detail. However, this problem can be overcome in a slightly modified design in another accelerator known as synchrocyclotron. # I have given here just a flavour about some basic accelerators, which are under routine use in different laboratories across the globe to generate accelerated particles. In India you will find such accelerators in the laboratories like Inter University Accelerator Centre (IUAC), New Delhi, Variable Energy Cyclotron Centre (VECC), Kolkata, Indira Gandhi Centre for Atomic Research (IGCAR), Kalapakkam etc. where basic researches on Nuclear Physics, Materials science, Atomic physics, Bio physics etc. are in progress. Apart from these accelerators there are some other accelerators, like, storage ring, particle collider, laser driven accelerators etc. where the energy of the particles can be increased upto GeV (10 9 eV) to TeV (10 1212 eV) range or higher are also available in different laboratories across the globe. The high energy nuclear physics or particle physics research is going on using these accelerators. You might have heard about large hadron collider (LHC), where experiments are in progress to get the signature of ‘Higgs boson’. |
| —————————————————————————————————————– *According to Einstein’s special theory of relativity, when a particle attains velocity comparable to that of light, the energy driven to the particle causes enhancement of mass and contributes very little to the increase in velocity. In the particle accelerators, the basic equations get modified by relativistic one, when particles attain very high velocity in the accelerator. |
| # The limitation imposed on the action of the cyclotron due to relativistic gain of mass can be compensated by proper adjustment of frequency in the dees. This is carried out by mechanically rotating capacitor whose capacitance varies periodically and imposes the necessary frequency modulation. These types of accelerators are known as the synchrocyclotron or frequency-modulated cyclotrons. ——————————————————————————————————————- |