A new method of significant efficiency enhancement, which is based on simultaneous interaction of electrons with an opposite wave at the second cyclotron harmonic, and a forward wave of the same frequency, at the fundamental cyclotron resonance, is proposed for the backward wave oscillator (gyro-BWO). Excitation of the forward wave results in significant efficiency enhancement, whereas the opposite wave provides a broadband feedback. This allows realizing a high-efficiency, frequency-tunable oscillator. Index Terms-Broadband gyro-oscillator, cyclotron resonance maser, gyro-BWO, gyro-TWT. )Fil: Moreno, Cesar Hugo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados. Provincia de Buenos Aires. Gobernación. Comision de Investigaciones Científicas. Grupo de Plasmas Densos Magnetizados; ArgentinaFil: Bruzzone, Horacio. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados. Provincia de Buenos Aires. Gobernación. Comision de Investigaciones Científicas. Grupo de Plasmas Densos Magnetizados; ArgentinaFil: Martínez, Javier. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados. Provincia de Buenos Aires. Gobernación. Comision de Investigaciones Científicas. Grupo de Plasmas Densos Magnetizados; ArgentinaFil: Clausse, Alejandro. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados. Provincia de Buenos Aires. Gobernación. Comision de Investigaciones Científicas. Grupo de Plasmas Densos Magnetizados; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentin

Bruzzone, Horacio

Clausse, Alejandro

Martínez, Javier

Moreno, Cesar Hugo

IEEE Transactions on Plasma Science

English

LAReferencia - Red Federada de Repositorios Institucionales de Publicaciones Científicas Latinoamericanas

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 5, OCTOBER 2000 1735Conceptual Engineering of Plasma-FocusThermonuclear PulsorsCésar Moreno, Horacio Bruzzone, Javier Martínez, and Alejandro ClausseAbstract—The basic engineering criteria for conceptual designof plasma focus devices is derived from a thermonuclear model,and applied successfully to the operation of small neutron pulsors.The theory is able to explain the variation of the neutron yield withthe gas pressure in deuterium-filled chambers, the current evolu-tion, and the electrode geometrical parameters. The performanceof a prototype designed to optimize the flux/fluence ratio is pre-sented, contrasting the experimental outcomes with the model. Aset of effective design parameters is deduced, which ensure a bandconfidence of 20%.Index Terms—Current sheet, fusion, neutrons, plasma-focus,plasma pinches, pressure dependence, thermonuclear,-pinch.I. INTRODUCTIONPLASMA neutron pulsors are small thermonuclear devicesbased on the pinch phenomenon occurring during the pathof high electric currents through gases. Essentially, the plasmapinch is a very fast compression and the consequent heating ofthe plasma by means of the associated magnetic field, duringwhich substantial amounts of different types of radiation areproduced, namely, x-rays, electrons, ions, and, using deuterium,neutrons from nuclear reactions. Different types of configura-tions can be used to induce the pinch formation: plasma focus,-pinch, -pinch, among others. To the present, the plasma focushas been the most successful device from the point of view ofneutron generation.Since the pioneer work of Filipov [1] and Mather [2], plasmafocus (PF) has been extensively studied by research laboratoriesaround the world, where several devices have been developedover the years aiming to increase the neutron emission [3], [4].Currently, PF pulsors are among the cheapest available neutrongenerators, with unique features of extremely short pulses (hun-dreds of nanoseconds) that suit them for a number of interestingapplications [5].In spite of the accumulated experience in operating plasmapinches over the last 30 yr in a wide range of energies, withremarkable success in producing neutrons, there is still contro-versy regarding the physical mechanisms involved in the pinchphenomenon. Most of the studies performed in PF pulsors areempirical, and not many theoretical calculations have been donein order to build a base for reliable design models. The numer-ical analysis reported in the literature [6], [7] are generally re-lated to the plasma acceleration process, whereas little attentionManuscript received March 7, 2000; revised July 6, 2000.The authors are with the National Research Network PLADEMA, Interin-stitutional Program of Dense Magnetized Plasmas, Tandil, 7000 Argentina(e-mail: clausse@exa.unicen.edu.ar).Publisher Item Identifier S 0093-3813(00)09977-X.Fig. 1. Diagram of the plasma focus phenomenon.has been paid to the neutron production and its relation to thecurrent, filling pressure, and other operating conditions.In this paper, a theoretical and experimental study of the neu-tron emission in PF pulsors is presented. A conceptual modelis produced, which accounts for the features that would be ex-pected if neutrons come exclusively from thermonuclear reac-tions. The theory is able to explain the relation of the neutronproduction with the gas-filling pressure, the current evolution,and the geometrical parameters of the device. A set of experi-ments was designed in order to compare with the model, leadingto good agreements. The model also shows good performanceagainst other experiments reported in the past. Finally, a set ofdesign criteria is recommended for the conceptual design of PFneutron pulsors.II. M ODEL OF THERMONUCLEAR PLASMA-FOCUSPlasma focus is a phenomenon occurring at the open end ofcoaxial electrodes when an intense electrical discharge betweenthem is induced by external means. Fig. 1 shows a scheme ofthe system. Two coaxial electrodes are located inside a vacuumchamber filled with deuterium gas at low pressure (neutronswere reported from 0.1 to 10 mbar). A charged capacitor bankis connected to the closed end of the electrodes through a switch(spark-gap). After closing the switch, a gas discharge starts inthe gap between the electrodes forming an umbrella-like plasmalayer. The azimuthal magnetic field located in the torus enclosedby the current produces a force that pushes the sheathtoward the open end of the electrodes. The rundown of the cur-rent sheet is a sweeping supersonic shock that propagates andcollects with certain efficiency the gas particles ahead of the0093–3813/00$10.00 © 2000 IEEE1736 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 5, OCTOBER 2000Fig. 2. IdealZ-pinch.front (snowplow scenario). On its arrival at the open end (somemicroseconds after triggering), the magnetic field starts to con-tract, accelerating the plasma toward the axis (runover stage).Finally, the sheath clashes on the axis in the form of a smalldense plasma cylinder (focus). The lifetime of the focus is about300 ns.A. Radial Plasma PinchLet us consider an ideal cylindrical pinch of autocompresseddeuterium plasma (Fig. 2), producing thermonuclear reactionsduring a short period of time when the density and tempera-ture are sufficiently high. The total yield production during suchpulse is given by (see Table I)(1)Equation (1) can be calculated provided that the time de-pendence of the deuteron density, the thermal cross section, and the pinch volume is known. Ideally, the pinch com-pression can be described as a nonlinear oscillator, where theLorentz force competes with the kinetic pressure from the gas.Assuming a constant electrical currentflowing axially alongan adiabatic plasma cylinder, the radial acceleration is given by(2)The parameters and in (2) are reference values of pres-sure and radius along an isoentropic transformation. The radiusfor which the right-hand side of (2) vanishes (Bennett equi-librium) is given by(3)The corresponding Bennett temperatureis(4)A useful assessment of the integral in (1) can be produced byassuming that during the reactive period the variables remainclose to the Bennett equilibrium. Using this assumption, (1) be-comes(5)where the subscript refers to the Bennett equilibrium.TABLE IPARAMETERS USED IN THE MODELThe effective thermonuclear cross section is a functionof the ions temperature according to(6)where .The characteristic time of the pinch is calculated as thehalf period of the harmonic oscillator associated with the lin-earization of (2) around the Bennett equilibrium, that is(7)Taking into account (7) and (4), the pinch duration results:(8)Combining (3)–(8) leads to(9)MORENOet al.: CONCEPTUAL ENGINEERING OF PLASMA-FOCUS THERMONUCLEAR PULSORS 1737Fig. 3. Graphic of (11).The Bennett radius is related to by means of the isoen-tropic hypothesis, that is(10)where is an appropriate isoentropic reference value.Combining (9) and (10), can be written in terms of onlyone variable :(11)Equation (11) leads to a remarkable conclusion regarding theefficiency of thermonuclear pinches. There is a critical pinchtemperature that produces the maximum neutron yield (seeFig. 3). Further efforts to increase the number of thermonu-clear reactions by improving the pinch compression would bein vain once is reached, since higher pinch temperatureswill reduce the efficiency. The maximum neutron yield occurs at. The ideal optimum neutron yield correspondingto this maximum is given by(12)where the characteristic current is defined as(13)The value of for deuterium plasma is about 88 kA.B. Dynamics of the Plasma GunConsider now a PF device. As a first approximation, one canregard the final radial collapse as an ideal pinch, accepting (2)as valid in this stage. However, the currentacting during thepinch is determined by the initial axial stage.Let us assume a one-dimensional (1-D) lumped model of anannular current sheet, coupled with an external electric circuitwhose main elements are a capacitor and some inductance. Con-sidering an initial charge in the capacitor and assuming aninstantaneous ideal dielectric breakdown, the governing equa-tions of the system are given by(14a)(14b)The solutions to first order are(15)(16)The optimum timing is achieved if the peak currentoccurs simultaneously with the pinch . Thus, thecondition for the optimum timing is approximately(17)If (17) is not satisfied, the current at the pinch would be lessthan , and consequently, the neutron yield would not beoptimum. Provided that , and are fixed, (17) can be tunedup by changing the initial deuterium pressure. In effect,andare related by(18)The current at the pinch for any given pressure is givenby(19)where is related to by means of (16) and (18), with .III. EXPERIMENTAL STUDYA PF pulsor prototype (GN1) was built in order to test thevalidity of the design model against reliable experimental data.The pulsor was designed to enhance the flux/fluence ratio byminimizing the size of the gas chamber. Fig. 4 shows the dia-gram of the experimental apparatus. The main parameters aregiven in Table II.Series of measurements were conducted at several deuterium-filling pressures in the range 2–7 mbar. The time derivative ofthe current flowing to the anode and the voltage across theelectrodes were monitored for each shot by a Rogowski coiland a resistive voltage divider, respectively, and were registeredusing a 500-MHz, 1-Gs/s digitizing oscilloscope. The time-in-tegrated neutron yield was also measured for each shot by silveractivation response. The neutron detector was placed at 60 cmfrom the focus in a line perpendicular to the axis. The neutronmeasuring system was calibrated by comparison against TLDdetectors.The timing from the current onset to the focusing time wasmeasured from both the and waveforms. Fig. 5 shows1738 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 5, OCTOBER 2000Fig. 4. Diagram of the prototype GN1.TABLE IIPARAMETERS OFGN1typical signals for filling pressures of 2, 4, and 6 mbar. Veryintense voltage spikes are obtained at the time where the max-imum compression takes place, thus indicating good focusing.It can also be observed that, as expected, the focus occurs laterfor higher pressures. Fig. 6 shows the average dependence ofthe focus timing with the deuterium pressure. The snow-plowtheory presented in Section II-B corresponds to the curve shownin Fig. 6, showing excellent agreement with the experimentaldata.Fig. 7 shows the dependence of the average neutron yieldper pulse with the filling pressure. The curve corresponds tothe model derived in Section II (4), (11), (16), (18), and (19)showing agreement within 20% of confidence.Fig. 5. TypicaldI=dt (dotted line) andV (solid line) signals measured inprototype GN1 for several filling pressures.Fig. 6. Dependence of the focus timing with the deuterium filling pressure(GN1).h = r ; r =h = 2:6 10 ;  = 0:17;  = 0:07.A. Benchmarking Against Other Experimental DataTwo sets of experimental data from similar experiments re-ported elsewhere were compared with the theory, in order tossess the scope of the effective parameters. The data were se-lected from reports of low energy PF pulsors available in theopen literature. Table III gives the main parameters of the ex-periments.Figs. 8 and 9 show the dependence of the average neutronyield with filling pressure. The theory performs remarkably wellusing similar effective parameters.Beg et al. [8] have carried out an interesting study that isvery useful for the conceptual design of PF pulsors. The neutronyield dependence with pressure was studied using ten differentMORENOet al.: CONCEPTUAL ENGINEERING OF PLASMA-FOCUS THERMONUCLEAR PULSORS 1739Fig. 7. Dependence of the average neutron yield with the deuterium fillingpressure (GN1).h = r ; r =h = 2:6 10 ;  = 0:17;  = 0:07.TABLE IIIPARAMETERS OFREPORTEDDEVICESFig. 8. Dependence of the average neutron yield with the deuterium fillingpressure [8].h = r ; r =h = 6:110 ;  = 0:57;  = 0:057.anode lengths. Figs. 10 and 11 show the maximum neutron yieldand the corresponding optimum filling pressure for each anodelength. It can be seen that the model is able to follow the exper-imental trend within the confidence bars.Nowikowski [9] measured the average neutron yieldchanging the initial bank voltage at fix pressure. Fig. 12 showsthe experimental data compared with the model, which again isable to follow the observed trend.IV. OPTIMUM DESIGN CRITERIONEquations (4) and (17) can be combined to derive an optimumdesign criterion for thermonuclear plasma focus devices. Equa-Fig. 9. Dependence of the average neutron yield (90 ) with the deuteriumfilling pressure [9].h = r ; r =h = 510 ;  = 0:7;  = 0:07.Fig. 10. Optimum neutron yield (90 ) for different anode lengths [8].h =r ; r =h = 6:110 ;  = 0:57;  = 0:057.Fig. 11. Optimum filling pressure for different anode lengths [8].h = r ; r =h = 6:110 ;  = 0:57;  = 0:057.tion (4) states that the number of deuterons per unit length thatshould be contained in the pinch to produce the optimum tem-perature is(20)1740 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 5, OCTOBER 2000Fig. 12. Dependence of the neutron yield (90 ) with the charge voltage [9].h = r ; r =h = 510 ;  = 0:7;  = 0:07.Fig. 13. Mass accumulated in the pinch.On the other hand, the mass per unit length that should becollected in the axial region to induce the peak current at thepinch is, according to (17)(21)Both magnitudes in (20) and (21) are proportional to thefilling gas density . In particular(22)and, assuming that the final pinch contains mostly the gas sweptduring the radial stage (see Fig. 13)(23)Combining (20)–(23), the condition for the optimum designproducing the peak current at the pinch and the optimum pinchtemperature simultaneously is given by(24)Fig. 14. Neutron yield dependence with the filling pressure and the electrodelength, for the GN1 device.where(25)and the characteristic lengthis defined as(26)Fig. 14 shows the neutron yield dependence with the anodelength and the filling pressure in GN1. The optimum yield isachieved when the peak current occurs simultaneously with thepinch and the condition given by (24).V. CONCLUSIONAn analytical model of thermonuclear model of plasma focusdevices is derived from the snowplow assumption and an isoen-tropic pinch oscillator. The model explains very well the fillingpressure dependence data of three experiments performed indifferent devices. The results show that the hypothesis of ther-monuclear reactions as the main source of the neutrons seemsto be sufficient for obtaining most of the measured features ofthe neutron yield.It is true that there is a significant literature, especially fromEurope, that clearly shows the existence of beam-driven fusionreactions in the plasma focus. However, it is also clear that theGN1 device in this paper is being operated in the high pressureregime. Thus, a better comparison is with the Mather group liter-ature from Los Alamos in the 1960s. That group clearly showeda scaling dependence of the fusion yield proportional to the cur-rent to the fourth.A possible interpretation of what happened with the beamsand beamlets inside the focus can be obtained by observing thatthe equilibrium times go aswhere and stand for the ion–electron and ion–ion equi-librium times.Therefore, as the current increases, beam contributions to thefusion yield via beam-hot target interactions become heatingcontributions to the core pinch.MORENOet al.: CONCEPTUAL ENGINEERING OF PLASMA-FOCUS THERMONUCLEAR PULSORS 1741The supporting evidence presented in this paper does not pre-clude interpretation by other models, but the model set out heredoes at least facilitate the raising of hypothesis, and offers asimple conceptual design criterion of plasma focus devices.ACKNOWLEDGMENTThe authors wish to thank two anonymous reviewers for theircomments and observations that help to enhance the quality ofthe paper.REFERENCES[1] N. V. Filippov, T. I. Filippova, and V. P. Vinogradov, “High temperaturedense plasma in a non-cylindricalz-pinch,”Nucl. Fusion Suppl., vol. 2,p. 577, 1962.[2] J. W. Mather, “Investigation of the high energy acceleration mode in thecoaxial gun,”Phys. Fluids Suppl., vol. 7, pp. 28–34, 1964.[3] A. Bernard, P. Cloth, H. Conrads, A. Coudeville, C. Gourlan, A. Jolas, C.Maisonnier, and J. P. Rager, “The dense plasma focus: A high intensityneutron source,”Nucl. Instr. Meth., vol. 145, pp. 191–218, 1977.[4] H. Conrads, “Dense plasma focus as a neutron source for fusion re-search,”Nucl. Sci. Eng., vol. 106, pp. 299–307, 1990.[5] G. Decker and R. Wienecke, “Plasma focus devices,”Physica, vol. 82C,pp. 155–164, 1976.[6] D. E. Potter, “Numerical studies of the plasma focus,”Phys. Fluids, vol.14, pp. 1911–1924, 1971.[7] L. Bilbao, H. Bruzzone, and H. Kelly, “Structure of a plane and sta-tionary ionizing current sheath,”Plasma Phys. Contr. Fusion, vol. 26,pp. 1535–1548, 1984.[8] F. N. Beg, M. Zakaullah, M. Nisar, and G. Murtaza, “Role of anodelength in a Mather-type plasma focus,”Modern Phys. Lett., vol. B6, pp.593–597, 1992.[9] J. Nowikowski, “Preliminary investigations of a non-cylindrical z-pinchsupplied from a 25 kJ current generator,”Nukleonica, vol. 20, pp.1081–1085, 1974.César Morenoreceived the M.Sc. and Ph.D. degrees in physics from the Uni-versity of Buenos Aires, Buenos Aires, Argentina, in 1989 and 1995, respec-tively, working on Plasma Focus discharges.Between 1995 and 1998, he was with the Colorado State University, FortCollins, working in X-ray lasers. Since 1999, he has headed the neutron gener-ators project of the Interinstitutional Program of Dense Plasmas, Buenos Aires.His current interests are with compact plasma focus andz-pinch devices andtheir applications.Horacio Bruzzone received the M.Sc. and Ph.D. degrees in physics from theUniversity of Buenos Aires, Buenos Aires, Argentina, in 1967 and 1976, respec-tively.From 1981 to 1998, he was Associate Professor of Physics with the Uni-versity of Buenos Aires and headed the experimental plasma physics group atthe Institute of Plasma Physics, Buenos Aires. Since 1999, he has headed theFast Pulsed Discharges Laboratory, University of Mar del Plata, Mar del Plata,Argentina. He is currently chairman of the scientific committee for the Interna-tional Centre on Dense Magnetized Plasmas (Poland) and fellow of the NationalScience and Technology Council of Argentina (CONICET). His research inter-ests are plasmas produced using fast pulsed discharges, with emphasis in PlasmaFocus andZ-pinch devices.Javier Martínez received the M.Sc. degree in physics in 1996 from the Univer-sity of Buenos Aires, Buenos Aires, Argentina. He is currently FOMEC grad-uate student in the same university, majoring in physics of pulsed electrical dis-charges and their applications.Alejandro Clausse received the nuclear engineering degree in 1981 and thePh.D. degree in 1986 from Instituto Balseiro, Bariloche, Argentina.He is Professor of Nuclear Engineering at the University of Cuyo, Cuyo, Ar-gentina, and Professor of Computer Science at the University of the Center,Buenos Aires, Argentina. He was Visiting Scholar at the Rensselaer PolytechnicInstitute, Troy, NY, from 1987 to 1990. Currently, he heads the PLADEMACenter of the Interinstitutional Program of Dense Plasmas, and the advancedreactors program of the National Atomic Energy Commission, Argentina.Dr. Clausse is fellow of the National Science and Technology Council of Ar-gentina (CONICET).

Conceptual Engineering of Plasma-Focus Thermonuclear Pulsors

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Conceptual Engineering of Plasma-Focus Thermonuclear Pulsors

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