Global Science and Technology Journal Vol. 5. No. 1. September 2017 Issue. Pp. 16-22 Structural Modifications of Cyclotron to Produce New Therapeutic & Diagnostic Particles BimanTanvir Ahmed *, Ramit Azad **, Masum Rabbani ** and Sayful Islam *** 1. Introduction This paper gives an idea of structural modification of discharge method of cyclotron to get better outputted energy to produce more radio-isotopes for various purposes. Without having major structural modifications only exchange of discharge method from electro-cyclotron resonance to beam plasma discharge with mirror magnetic trap confines about 10 4 more volumetric charge particles which ensure more outputted energy of the cyclotron. This is a theoretical analysis to make some structural modifications to cyclotron to improve production capability enhancing more energy to get more nuclear reactions with targeted particles. If we consider the cyclotron as vacuum chamber with permanent magnetic contour; we can assume that the primary acceleration of electrons occur due to electro-cyclotron resonance of plasma and therefore goes to the system of Dees to be accelerated further more. Cyclotrons with different specified acceleration energies cannot undergo heavy modification due to its constructional limitation; such as RF frequency, Magnetic contour-made by permanent magnet, volume constancy of vacuum chamber, etc. If we introduce to the system the beam plasma discharge parameters: like cylindrical electron gun with high voltage, magnetic field made by coils of mirror-like magnetic trap and some vacuum parameters instead of exiting RF source, magnet, we can upgrade the output acceleration energy of the cyclotron without further structural modifications. The importance of this theoretical analysis consists the way of up gradation of existing cyclotrons to higher energy without heavily structural modifications and also gives the idea to manufacturers to make more energized cyclotrons with more regularity of input parameters as because change of the discharge method from ECR to Beam plasma discharge into mirror magnetic trap can generate about more 10 3 energized particles. The paper is organized as follows: section 1 deals with introduction and section 2 focuses on literature review on two types of discharge methods and their applications. Section 3 contains methodology in which formulation of the problem, mechanisms of two types of the discharge methods are been described and been proposed the structural modifications to change the discharge method from ECR to Beam plasma discharge. Results which might be achieved are been shown after having the proposed modifications in section 4. At last, in section 5 the conclusion is drawn in which plotted the limitations of the work and the future scope of research. * Corresponding author, National Institute of Nuclear Medicine and Allied Sciences, Bangladesh Atomic Energy Commission, Dhaka, Bangladesh, Email: biman_ahmed@yahoo.com ** American International University Bangladesh, Dhaka, Bangladesh, Email: ramit_azad@mail.ru *** Jagannath University, Dhaka, Bangladesh. 16
2. Literature Review Ahmed, Azad, Rabbani & Islam So we like to discuss some of works demonstrate the possibility to obtain the hot electrons in beam plasma discharge. It is shown in work (Shapkin et al,1968) that the high-energy electrons are generated in a mirror magnetic trap with high mirror ratio at the interaction of electron beam with cold plasma with density 10 12 cm -3 in volume of 20 liters. The temperature of high electron component was 200 kev, the plasma density was 2 x 10 10 cm -3. The plasma with electron temperature 550 kev and density of 10 11 cm -3 in volume of 4.2 liters was produced in installation PN-2 by means of adiabatic plasma compression (Shapkin et al, 1972). The intensive of X-ray radiation in the experiment was up to 1 MeV. The hot plasma was confined by mirror magnetic field without decay for a few seconds in the experiment. The powerful beam-plasma amplifier is described in work (Shapiro et al,1994). The amplifier is manufactured as a separate vacuum device. In the amplifier the accelerating voltage of electron beam was U 0 = 15 25 kv, the beam current was I = 3 5 A, the strength of magnetic field of a solenoid was 2 3 koe, the pressure rang of working gas (hydrogen) in the interaction space was 10-6 10-3 Torr. Thus, the existence of physical processes of electron heating up to relativistic energies in plasma of the beam-plasma discharge was experimentally tested at the end of 60 th at the beginning of 70 th (Ivanov, 1995). At the beginning of 90 th the experimental researches were executed with the standalone device on the base of the beam-plasma discharge. To compare two discharge methods with mirror magnetic trap we also (Vodopyanov et al, 2011) where to realizing high plasma parameters in electron cyclotron resonance discharge supported by microwave radiation in axisymmetric magnetic trap has been proposed. For generally electron heating by electro-cyclotron resonance was been observed through the academic dissertation of Olli Tarvainen, Finland, 2005. 2.1 Notation and Problem Formulation Analyzing two types of discharge methods of plasma heating, one is electro-cyclotron resonance and the other is beam plasma discharge we can get some interesting findings which can be the arguments to get some structural modifications to the existing cyclotron system. We can consider the cyclotron as vacuum chamber with permanent magnetic contour; we can assume that the primary acceleration of electrons occur due to electro-cyclotron resonance of plasma. Principe of heating electrons with electrocyclotron resonance is interaction of radio frequency wave with plasma at magnetic contour; where extracted electrons from plasma take part into interaction with Langmuir oscillator at the magnetic contour with resonance frequency of RF. On the other hand, in case of beam plasma discharge in mirror magnetic trap the strong beam plasma interaction takes place and it results in the growth of the cross size of plasma and in the strong heating of the hot electrons confined by the trap. The electron beam excites the Langmuir oscillation at the interaction with plasma. The heating of hot electrons take place because of its interaction with the electron Langmuir oscillation ω Pe > ω He. The density of heated electron with ECR is about 10 10 cm -3 ; where the density of heated electrons with beam plasma discharge is about 10 14 cm -3. More density associates more output energy and thus produce more therapeutic & diagnostic particles with nuclear reactions. In case of beam plasma discharge there are some regulations of choosing 17
discharge parameters. So introducing to the cyclotron the beam plasma discharge parameters: like cylindrical electron gun with high voltage, magnetic field made by coils of mirror-like magnetic trap and some vacuum parameters instead of exiting RF source, magnet, we can upgrade the output acceleration energy of the cyclotron without further structural modifications. 2.2 Mechanism of Electron Heating in Electro Cyclotron Resonance In an ECR ion source ions are produced in magnetically confined plasma, which is heated by microwaves. Plasma can be practically defined as: a quasi neutral gas that exhibits collective behavior when exposed to external electromagnetic fields. It is of note that plasma also exhibits collective behavior via long range Coulomb interaction. There is no well-defined phase transition point from the gaseous state to plasma that consists of electrons, ions and neutral atoms or molecules. The most significant difference between plasma and neutral gas is the number of freely moving charges that make plasma a good conductor. Plasma also has properties that are characteristic of liquids, for example it is nearly incompressible. Ionized gas can be considered as plasma if the following so-called plasma conditions are fulfilled: (i) (ii) (iii) The typical length scale (dimension) L of plasma has to exceed the shielding length λ D (Debye length) of the plasma. The Debye length determines how far the charge. Imbalance due to thermal motion in the equilibrium state or the impact of an external electric potential can extend in plasma or in ionized medium. The condition can be written for electrons as =..(1) where ε 0 is the permittivity constant ( 8.854 10-12 F/m), k the Boltzmann constant ( 1.38 10-23 J/K), Te the electron temperature (in Kelvin), e the elementary charge ( 1.602 10-19 C) and ne the electron density. If this condition is not valid, the plasma is not necessarily macroscopically neutral. In order to have collective behavior, the number of particles inside the Debye sphere must be sufficient i.e. 1 (2) The frequency f pe of collective plasma (electron) oscillations must be higher than the collision frequency ν en of electrons and neutrals = = >.(3) where me is the electron mass ( 9.11 10-31 kg). Equation (3) defines the plasma oscillation frequency ωpe. If this plasma condition is not valid, there are no collective phenomena and the dynamics of the system is dominated by the motion of neutrals. This condition is fulfilled as the degree of ionization of the plasma increases. Usually ionized gas can be considered to be plasma when its degree of ionization exceeds a few percent. 18
The propagation of electromagnetic waves and electron heating in the plasma of ECR ion sources is not completely understood. This is due to the unique magnetic field structure, varying plasma density, boundary conditions set by the plasma chamber walls, resonance(s) and cut-offs. In order to treat the problem analytically, simplifications such as linearization, single-particle theories, cold plasma approximations and diagonalized plasma pressure tensors are normally used. The propagation of magneto hydrodynamic waves in the plasmas has been omitted in the following since their importance in the case of electron heating in ECRIS plasmas is minor. The wave propagation can be described with the aid of the Lorentz force and the wave equation derived from Maxwell s equations: = ( + ).(4) = ( + ).(5) where is the electron velocity, the electric field of the wave, the external magnetic field, the wave vector, ω the microwave frequency, c the velocity of light ( 2.998 108 m/s) and = the current density. In order to derive the resonance condition for electron cyclotron resonance it is sufficient to consider only the propagation of electromagnetic waves parallel to the external magnetic field. Waves propagating perpendicular to the external magnetic field would result in upper hybrid resonance (UHR), which will not be considered here since there is no evidence on their importance in ECRIS plasmas. The phase velocity, vp, of the wave propagating parallel to external magnetic field can be derived from equations (4) and (5). = ± = ±.(6) The plasma oscillation frequency ω pe can be determined from equation (3). Here the + sign corresponds to so-called L-wave (left-hand polarized) and sign to so-called R- wave (right-hand polarized). In electron cyclotron resonance the electrons are heated by the R-wave. Under the correct conditions the L-wave would heat ions in ion cyclotron resonance (MHz-range). However, there is no ion cyclotron resonance in ECR ion sources and therefore only the R-wave will be considered. Equation (6) shows that the R-wave can propagate (phase velocity is not imaginary) in magneto plasma if 0< > = (7) When ω= ωce the gyration of electrons is in resonance with the electric field of the wave, which is the resonance condition for electron cyclotron resonance. Equation (7) shows that the phase velocity of the wave in the resonance. Therefore, the cold plasma theory is not applicable when determining the behavior of the wave in the close 19
proximity of the resonance. At the point where ω= ω 0 p vco so-called cut-off occurs preventing wave propagation through the cut-off. The cut-off frequency depends not only on the external magnetic field but also on the electron density of the plasma. The electron density of an ECRIS plasma is typically on the order of 10 11 cm -3 though there is spatial variation. 2.3 Mechanism of Electron Heating by Beam Plasma Discharge The analysis of the experiment and theoretical researches of the beam heating of electrons in mirror magnetic trap is resulted in work. When the electron beam is injected in mirror magnetic trap the strong beam plasma interaction takes place and it results in the growth of the cross size of plasma and in the strong heating of the hot electrons confined by the trap. The electron beam excites the Langmuir oscillation at the interaction with plasma. The heating of hot electrons take place because of its interaction with the electron Langmuir oscillation ω Pe > ω He. The width of the beam in the space of velocities v becomes to the initial velocity of the beam u at distance 20 to 30 cm from the beam input in the system. The characteristic increment of instability is γ ω Pe n 0b /n 0. The electron beam excites the oscillations are mainly with wave of vectors parallel to its axes. The spectrum of Langmuir oscillation is essentially non isotropic. If the electrons at interaction with noise will not get in a cone of losses in the space of velocities, they will diffuse in usual space to the periphery of the installation and its energy will slowly increase. The cone losses in the space of velocities are the function of mirror ratio R. Thus, to obtain hot electrons it is necessary to satisfy the series of conditions for the confinement of electrons in mirror magnetic trap and for their heating up to high energies, namely: ω Pe > ω He (8), γ ω Pe n 0b /n 0 (9), R> 1/cos 2 θ 0 (10), Where arctgθ = k /k, and θ 0 is some limiting angle. If to take into account, that the radius of a beam a 1, and characteristic wave vector of raised oscillations k ω Pe / u 5 cm -1, that k a >>1. It means that for estimation it is possible to use outcomes of the theory of a boundless beam. Energy of oscillations in a transverse direction is transferred with formation speed =. The time of propagation of oscillations up to diaphragms limiting plasma is much less then decay time on hot particles. At on frequency, wave number k and the speed of hot electrons v is superimposed a condition =csc, where φ is an angle between k and v. The vigorous electron will be effective to interact only with those oscillations, which wave number is perpendicular to their velocities. 20
On the base of the above one can observe the dependence of the energy of hot electrons on the strength of the magnetic field. The electrons involved in process of acceleration increase the energy and diffuse from a beam to an exterior wall of the trap. The energy of electrons is determined by the time of its life in trap τ. =( + ), where is the time of dispersion in a cone losses, and is the time of diffusion of an electron up to the external boundary of plasma. 2.4 Structural Modification To get more energized protons for getting more nuclear reactions (a long range of average energy of the nuclear activation) with the various targets we have to change primary acceleration of particles into the cyclotron from ECR to beam plasma discharge with mirror magnetic trap. As we know that beam plasma discharge is a volumetric acceleration and through this the amount of accelerated particles overcomes almost thousand times from ECR; so if we change the discharge method by changing ion source, magnetic field and discharge parameters like vacuum we can get accelerated particles as our desire. Figure: Magnetic Field for Cyclotron (Electro-Cyclotron Resonance) and the Replacement of the Magnetic Field (Beam Plasma Discharge with Mirror Magnetic Trap) 3. Results This is a theoretical analysis to make some structural modifications to cyclotron on basis of introducing beam plasmaa discharge parameters instead of exiting RF source, magnet, which are associated with electro-cyclotron resonance parameters. So the possibility to get heated electron density up to 10 14 cm -3 with mirror magnetic trap by beam plasma discharge could be executed instead of permanent magnet in existing cyclotron what might be the strong arguments to implement the structural modifications to improve production capability enhancing more energy to get more nuclear reactions with targeted particles. 21
4. Conclusion Theoretical analysis of making some structural modifications to cyclotron to improve production capability enhancing more energy to get more nuclear reactions with targeted particles on the basis of introducing beam plasma discharge parameters instead of exiting RF source, magnet, which are associated with electro-cyclotron resonance parameters confirmed us to do these modifications. Now the question of implementing these structural modifications of existing cyclotron is open to the manufacturers. If the manufacturers come to make structural modifications of their cyclotrons with further research then only we can get cost effectively high energized existing cyclotrons and new ones. References Ivanov, A. A. 1995, The present state and development trends of discharges, Physics and chemistry of plasmas phenomena in Ionized Gases (XXII ICPIG) Hoboken, NJ, July-August 1995, Pp. 41-74. Gospodchikov, E.D., Golubev, S.V., Smolyakova, O.B., Suvorov, E.V., and Vodopyanov, A.V. 2014, On the Possibility of ECR-Discharge with Overcritical Plasma Density in Axisymmetrical Magnetic Trap, Institute of Applied Physics RAS, Article in Fusion Science and Technology January, 2011 <https://www.researchgate.net/publication/266500202> Alexeff, I., Neidigh, R.V., Peed, W.F., Shipley, E.D. and Harris, E.G. 1963, Hot electron plasma by beam-plasma interaction, Phys. Rev. Letters, Vol. 10, No. 7, Pp. 273-276. Zakatov, L.P., Plakhov, A.G., R utov, D.D., and Shapkin, V.V. 1968, The research of a high-temperature electron component of plasma formed in the system a plasmabeam, JETPh, Vol. 54, No. 4, Pp. 1088-1098. Zakatov, L.P., Plakhov, A.G., R utov, D.D., and Shapkin, V.V. 1972, The obtaining of relativistic plasma by adiabatic compression in the system plasma-beam, Pisma v JETPh, Vol. 15, No.1,Pp. 16-20. Mitin, L.A, Perevodchikov, V.I., Zav alov, M.A., Tskhay, V.N., and Shapiro, A.L. 1994, Powerful microwaves wide band beam-plasma amplifiers and generators, Physics of plasma, Vol. 20, No. 7-8, Pp. 733-746. Tarvainen, O., 2005, Studies of Electron Cyclotron Resonance Ion Source, Plasma Physics, Department of Physics, University of Jyväskylä, Finland, Academic Dissertation for the degree of Doctor of Philosophy, December 2005, Pp. 45-47. Atamanov, V.M., Biman, T.A., Elizarov, L.I., Ivanov, A. A., Pereslavtsev, A.V., and Shubin, N.N. 2000, Hot Electrons in Beam-Plasma Discharge Problems of Atomic Science & Technology, Series: Plasma Electronics,. N:1, Ukrine, Pp. 46-49. 22