Possibility of Using Dense Plasma Focus Devices to Produce Short-Lived Radioisotopes Used in PET—Numerical Study

ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 166 ةريصق ةعشم رئاظن جاتنلإ ةفيثكلا ةيقرحملا امزلابلا ةزهجأ مادختسا ةيناكمإ يف ةمدختسملا رمعلاPET - ةيددع ةسارد فيصان ءلاع .د 1 .د .أينويهص ديلو 2 :صخلملا ةزهجأ مادختسا ةيناكملإ ةيددع ةسارد ءارجإ ثحبلا اذه يف مت جاتنإ يف ةفيثكلا ةيقرحملا امزلابلا ( رمعلا ةريصق ةعشملا رئاظنلاSLRs ةجتانلا مويريتويدلا تانويأ مزح نم ةدافتسلاا للاخ نم ) نيريظنلا ىلع ةساردلا تيرجأ .امزلابلا ةضبق رايهنا نعC^11 وO^15 ددع داجيإ مت ثيح ، عاعشلإا طاشنلا باسح مث نمو فدهلا عم ةلعافتملا تانويلأا ةجتانلا ميقلا ةنراقم للاخ نمو ،ي نم ةدافتسلاا مت ،ًادج ةضفخنم ميقلا تناك ،نورتولكيسلا اهجتني يتلا يعاعشلإا طاشنلا ميق عم تعفترا ثيح طغضلا ريغت دنع يعاعشلإا طاشنلا باسحو مويريتويدلا زاغ طغض رييغت ةيناكمإ ىلإ طاشنلا ةميق0.002 GBq و نوبركلل0.013 GBq جسكلأل نكلو طغضلا ةدايز عم ني تاقوأو تاددرت دنع يعاعشلإا طاشنلا باسح مت .ةبولطملا ةميقلا ىلإ لوصولا نم نكمتن مل دنع نوبركلل ةبولطملا ةميقلا ىلع انلصح .ةفلتخم ليغشت275 ،زتره1000 نيجسكلألو ،ةيناث دنع75 ،زتره1000 .ةيناث :ةيحاتفملا تاملكلا ،امزلابلا ةضبق ،ةفيثكلا ةيقرحملا امزلابلاPET ةريصق ةعشملا رئاظنلا ، .يعاعشلإا طاشنلا ،رمعلا ________________________ 1 ،روتكدايروس ،هامح ،ةصاخلا ةينطولا ةعماجلا ،ةلديصلا ةيلك 2 ،ذاتسأ ،صمح ،ثعبلا ةعماج ،ءايزيفلا مسق ،امزلابلا ثاحبأ ةدحو سيئرايروس ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 167 Possibility of Using Dense Plasma Focus Devices to Produce Short-Lived Radioisotopes Used in PET - Numerical Study Dr. Alaa Nassif 1 Prof. Dr. Walid Sahyouni 2 ABSTRACT: In this paper, a numerical study was conducted of the possibility of using dense plasma focus devices in the production of short-lived radioisotopes (SLRs) by taking advantage of the deuterium ion beams resulting from the collapse of the plasma pinch. The study was done on the two isotopes C^11 and O^15, where the number of ions interacting with the target was found and then the radioactivity was calculated. Comparing the resulting values with the values of the radioactivity when produced by the cyclotron, the values were very low, and by taking advantage of the possibility of changing the pressure of deuterium gas. The radioactivity was calculated when changing the pressure, as the activity value increased to 0.002 GBq for carbon and 0.013 GBq for oxygen with increasing pressure, but we could not reach the required value. The radioactivity was calculated at different frequencies and operating times. We obtained the required value for carbon at 275 Hz, 1000 s, and for oxygen at 75 Hz, 1000 s. KEYWORDS: Dense Plasma Focus, Plasma Pinch, PET, short-lived radioisotopes, radioactivity. ________________________ 1 Doctor, Faculty of Pharmacy, Al-Wataniya Private University, Hama, Syria 2 Professor, Head of Plasma Research Unit, Department of Physics, Al-Baath University, Homs, Syria ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 168 1. Introduction Positron emission tomography (PET) is a functional molecular imaging technique using probes called radiotracers that consist of biologically active molecules (glucose or oxygen). Labeled with positron-emitting radioactive nuclei (eg carbon 11, nitrogen 13, oxygen 15, fluoride 18); Where the positron travels for a short distance in the tissues until it collides with an electron and produces a pair of gamma rays that emit in opposite directions with an energy of 511 KeV each. By directly measuring the radioactivity of the member to be studied at large angles and distances. This method of radiography is one of the fastest growing areas of radiology [1,2]. Figure (1): Principle of PET scan: (a) injection of the radioactive isotope, (b) the positron travels a short distance and hits the electron and then a pair of gamma rays with an energy of 511 KeV simultaneously at 1800 each (c) Detecting gamma rays and converting them into three-dimensional images [1] It's known that these radioactive isotopes are obtained by bombarding suitable targets with ion beams produced in accelerators. Table (1) shows a number of radioactive isotopes that are obtained through accelerators and the radioactivity of each of them [3]: ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 169 Table (1): Some of the isotopes that are produced by the cyclotron, nuclear reactions and radioactivity [3] Due to the short half-life of these radioisotopes, they must be produced where they are expected to be used, and therefore accelerators must be used in hospitals. But the production of PET radioisotopes via accelerators is an expensive method, so plasma focus devices are offered as an alternative in the production of short-lived radioisotopes because they are low-cost and easy to use and maintain [4]. Dense Plasma Focus Device: The Dense Plasma Focus DPF device is a bidirectional ion accelerator. The device takes advantage of the Lorenz force F=J×B, where J is the current density and B is the magnetic field to accelerate the gas molecules, ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 170 which are axially swept by the plasma envelope at a high speed to a specific position (the end of the electrodes), the flow is then converted into a radial flow with a higher velocity and the formation of high-density filaments of plasma called the plasma focus [5]. The device is originally a coaxial accelerator [6] consisting of a chamber inside which a central electrode forms an anode surrounded by a group of electrodes that form a cathode isolated from each other by an insulator connected with a capacitor bank (The charge potential of a capacitor bank is several tens of kV), a chamber containing a gas or group of gases under a certain pressure. The principle of operation of the device is based on transferring the energy stored in the capacitor bank to the electrodes through a discharge current (up to several hundred kA in medium-power devices and up to MA in high-power devices) which generates a magnetic field. The induced magnetic field is stored behind an ionized layer of gas. A plasma sheath moving under the influence of a magnetic field is referred to as a magnetic piston [7]; this ionizing layer extends between the internal and external electrodes (the anode and the cathode) and is responsible for transmitting electric current between them. The ionized layer that carries the current is called the current sheet (Current Sheet CS). It represents the J component of the Lorenz force. The electric current passes through the cathode from its base to the position of the current sheet causing an angular magnetic field to be excited around the cathode in the angular direction (B_θ)as shown in Figure (2). The magnetic field is behind the current sheet, J_r and B_θ push the current sheet with a Lorenz force (F_z) to reach a high axial velocity of 10^7 cm/s which doubles in diagonal direction, and the density increases to reach 10^19/ 〖cm〗^3 to produce very plasma filaments with several energy. A small column of very hot and very dense plasma that collapses after a very short ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 171 period (tens of ns) due to the instability of the plasma and the presence of a high voltage, which leads to the emission of beams of ions and electrons in opposite directions [5]. Figure (2): Axial and radial motion of the current sheet in a dense plasma focus [5] In the case that deuterium gas is used in the dense plasma device, it is possible to take advantage of the energy ion beams produced after the collapse of the plasma pinch and its collision with a suitable target in order to cause the desired reaction. To this aim, many researche and experimental and numerical studies have been conducted to investigate the possibility of benefiting from the ion beams emitted by the collapse of a column of plasma formed in the dense plasma focus device, especially when using deuterium gas as a working gas in order to bring about the nuclear reaction required for the production of radioactive isotopes shortlive. Sumini [8] designed a 150 kJ dense plasma focus device operating in a 1 Hz frequency mode to produce the 18F radioactive isotope 1 Curi in a time of 2 hours and put the engineering designs of the electrodes and the parameters of the electrical circuit, and 128 shots were carried out. ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 172 Shirani [9] also studied the possibility of obtaining the radioactive isotope 13N from a low-energy dense plasma focus device, and the value of the radioactivity was obtained 10 kBq for one shot, and the value of the radioactivity increased to several tens of MBq from an operating rate of f=1Hz for an operating time of 600s, while the medically required radioactivity is about 4 GBq, the idea of changing the design of the electrodes or the pressure of deuterium gas was proposed to increase The energy of the outgoing detrons spectrum .Akel [10] conducted numerical experiments using the Lee code to calculate the characteristics of the ion beams emitted by a number of dense plasma devices with different operating energies and to calculate the radioactivity of the 12C(d,n)13N reaction, and that they concluded the device must operate in a repetitive mode (f=25Hz repetition rate for a period of 600s of operation) to reach the value of the medically required radioactivity and that this possibility of operation is not available in the current devices in addition to the emergence of the problem of endurance of targets for thermal loads resulting. In 2019, Sadeghi and others [11] proposed the idea of adding magnetic lenses in order to focus and direct the outgoing ion beams and reduce the scattering ratio, Simulations were carried out on 16 different plasma incinerators with different energies 400 J to 500 kJ and a radioactivity value of 0.016-7.71 GBq was reached, and that 9 of the studied devices had the ability to reach the medically required value of the isotope 13N by using this technique. 2. Research Method The most important factor in the production of short-lived radioisotopes using dense plasma focus devices is the number of deuterium ions from the pinch, which can be estimated by the potential generated in the pinch due to a sharp increase in plasma induction during the radial phase. The ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 173 Lee code was used to find the pinch parameters, and then the method followed by Razazi and Gharehbagh [12] was used to calculate the radioactivity as follows: The number of deuterium ions resulting from the collapse of pinch is calculated using the relation: 𝑁𝑜𝑢𝑡=π𝑟𝑝2 𝑒𝐽𝑖𝜏𝑝 (1) where: τp duration of pinch stays above the top of the anode, rp the pinch radius Ji is the density of ions, which is calculated by: 𝐽𝑖=4 9𝜀0(2𝑒 2𝑚𝑒)1/2(ϕ2 𝑧𝑚𝑎𝑥 2) 1+(𝑚𝑖 𝑚𝑒)1/2 (2) where: ε0 the electrical permittivity, e the charge of the electronme the mass of the electron, mi the mass of the deuterium ion, zmax the length pinch, ϕ the voltage generated within the pinch which is calculated by: ϕ=𝐼𝑚𝑎𝑥(𝑑𝐿 𝑑𝑡) (3) Imax is the current formed within the pinch, dL dt the induction within the pinch, and is calculated by: 𝑑𝐿 𝑑𝑡=𝜇0 2𝜋[𝑙𝑛(𝑏 𝑟𝑝)𝑉𝑎+𝑧 𝑟𝑝𝑉𝑟] (4) where: b is the radius of the cathode, Va is the axial velocity of the plasma sheet, Vr is the radial velocity of the plasma sheet. Calculate the number of radionuclides produced at each shot using the relation: 𝑁𝑝 =𝑁𝑜𝑢𝑡𝑛𝑡𝜏𝑝1 3.5−2√2 𝑀𝑑∫. 𝑚=3.5 𝑚=2 ∫1−𝑚 𝐸𝑚𝑎𝑥 1−𝑚−𝐸𝑚𝑖𝑛 1−𝑚𝜎(𝐸)𝐸−𝑚+1/2𝑑𝑚𝑑𝐸 𝐸𝑚𝑎𝑥 𝐸𝑚𝑖𝑛 (5) where: nt the target density, Md the mass of the deuterium ion, Emin and Emax, the minimum and maximum energy of the ions produced by the ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 174 collapse of the deuterium plasma pinch, m is a constant having the value 2<m<3.5, σ(E) is the cross-section of the studied reaction. The radiative yield of the reaction is calculated by: 𝐴=𝑁𝑝𝑙𝑛2 𝑇1/2 (6) The isotope 𝐂𝟏𝟏 : This isotope is obtained by the reaction B10(d,n)C11 where this reaction has a cross section given by [12]: σ10B(d,n)=2.797 Eexp(−236 √E );0<E<500 keV (7) 3. Results and Discussion The study was conducted on a number of dense plasma focus devices of different operating energy and geometric dimensions [13] as shown in the following table (2): Table (2): Parameters of the studied plasma focus devices [13,14,15,16,17,18,19,7] A series of numerical experiments were carried out using Lee code [20] version (RADPFV5.15de.c1) in order to find the characteristics of the plasma pinch (ion source) at the pressure value of deuterium gas 1 Torr. These features include: pinch dimensions (length and radius), plasma sheet velocity (axial and radial), pinch duration time, pinch current, and PF6 BORA INTI PF12 PF400 FMPF3 6.2 3.5 3.4 2.6 0.4 0.2 ( kJ) 0 E 28 24.4 30 20 1 2.4 ( µF) 0 C 21 54 110 80 40 34 ( nH) 0 L 2.9 6 12 6.0 10 11 ( cm) 0 r 5.1 2.5 3.2 2.7 1.6 1.5 Cathode radius (cm) 3 1.5 1 0.9 0.6 0.6 Anode radius (cm) 4 6 16 7.2 1.7 1.7 ( cm) 0 z 21 17 15 16 28 6.6 Voltage (kV) ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 181 device (PF6), the rate and operating time of the device must be increased to be 275 Hz and operating time of 1000 s in the case of C^11 and 75 Hz and a operating time of 1000 s in the O^15 state. 4. References 1. Yang L, Scott PJ, Shao X. [11C] Carbon Dioxide: Starting Point for Labeling PET Radiopharmaceuticals. InCarbon Dioxide Chemistry, Capture and Oil Recovery 2017 Dec 20. IntechOpen. 2. von Schulthess GK, Steinert HC, Hany TF. Integrated PET/CT: current applications and future directions. Radiology. 2006 Feb;238(2):405-22. 3. Schmor, P. W. "REVIEW OF CYCLOTRONS USED IN THE PRODUCTION OF RADIO-RADIOISOTOPES FOR BIOMEDICAL APPLICATIONS." (2010). 4. Saed M, Roshan MV, Banoushi A, Habibi M. The investigation capability of plasma focus device for 13N radioisotope production by means of deuteron experimental spectrum. Journal of Modern Physics. 2016 Aug 2;7(12):1512-8. 5. Mohamed AE. A dense plasma focus device as a pulsed neutron source for material identification. Kansas State University; 2015. 6. Mather JW, Bottoms PJ. Characteristics of the dense plasma focus discharge. The physics of fluids. 1968 Mar;11(3):611-8. 7. Lee S. Plasma focus radiative model: Review of the Lee model code. Journal of Fusion Energy. 2014 Aug;33(4):319-35. 8. Sumini M, Mostacci D, Rocchi F, Frignani M, Tartari A, Angeli E, Galaverni D, Coli U, Ascione B, Cucchi G. Preliminary design of a 150 kJ repetitive plasma focus for the production of 18-F. Nuclear Instruments and Methods in Physics Research Section ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 182 A: Accelerators, Spectrometers, Detectors and Associated Equipment. 2006 Jun 23;562(2):1068-71. 9. Shirani B, Abbasi F. Prospects for 13N production in a small plasma focus device. Journal of Fusion Energy. 2013 Apr;32(2):235-41. 10. Akel M, Alsheikh Salo S, Ismael S, Saw SH, Lee S. Interaction of the high energy deuterons with the graphite target in the plasma focus devices based on Lee model. Physics of plasmas. 2014 Jul 15;21(7):072507. 11. Sadeghi H, Amrollahi R, Fazelpour S, Omrani M. Simulation of dense plasma focus devices to produce N-13 efficiently. Laser and Particle Beams. 2019 Jun;37(2):209-16. 12. Razazi V, Gharehbagh RM. Activities study of PET's radioisotopes production with plasma focus devices. In2010 17th Iranian Conference of Biomedical Engineering (ICBME) 2010 Nov 3 (pp. 14). IEEE. 13. Lee S, Saw SH. Plasma focus ion beam fluence and flux—Scaling with stored energy. Physics of Plasmas. 2012 Nov 12;19(11):112703. 14. Lee S, Saw SH. Plasma focus ion beam fluence and flux—For various gases. Physics of Plasmas. 2013 Jun 19;20(6):062702. 15. SAW, S. H., LEE, S., Plasma Focus Numerical Experiments and BORA - Invited Workshop/Lecture presented at School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications, 8-12 October 2012, International Centre for Theoretical Physics, Trieste, Italy. ICTP 2370_6 (2012). ةصاخلا ةينطولا ةعماجلا ةلجم– دلجملا1 – ددعلا1 -2023 فيصان ءلاع .د 1 د.أ .ينويهص ديلو 2 183 16. Saw SH. Plasma focus ion beam-scaling laws. International Journal of Modern Physics: Conference Series 2014 Aug 13 (Vol. 32, p. 1460317). 17. Saw SH, Lee S. Multi-scaling of the dense plasma focus. InJournal of Physics: Conference Series 2015 Mar 1 (Vol. 591, No. 1, p. 012022). IOP Publishing. 18. Akel M, Salo SA, Saw SH, Lee S. Characterization of oxygen ion beams emitted from plasma focus. Vacuum. 2014 Dec 1;110:547. 19. Lee S, Saw SH. The slow focus mode in plasma focus for fast plasma stream nano-materials fabrication: selection of energy of bombarding particles by pressure control. J. Sci. Eng. Technol. 2014;10(11):17-23. 20. Lee.S., Radiative dense plasma focus computation package: RADPF.http://www.plasmafocus.net/IPFS/modelpackage/File1RADP F.htm. 21. Sadat Kiai SM, Adlparvar S, Sheibani S, Elahi M, Safarien A, Farhangi S, Zirak AR, Alhooie S, Mortazavi BN, Khalaj MM, Khanchi AR. Design a 10 kJ IS mather type plasma focus for solid target activation to produce short-lived radioisotopes 12C (d, n) 13N. Journal of fusion energy. 2010 Oct;29(5):421-6.