Experiment performed on plasma synchrotron Gyrac-X operating on synchrotron gyromagnetic autoresonance (SGA) is described. Gyrac-X is a compact plasma x-ray source in which kinetic energy of relativistic electrons obtained under SGA converts into x-ray by falling e-bunches on to a heavy metal target. The plasma synchrotron acts in a regime of a magnetic field pulse packet under constant level of microwave power. Experiments and numerical modeling of the process showed that such a regime allowed obtaining dense short lived relativistic electron bunches with average electron energy of 500 keV – 4.5 MeV. Parameters of the relativistic electron bunch (energy, density and volume) and dynamics of the electron bunches can be controlled by varying the parameters of the SGA process. Possibilities of x-ray intensity increase are also discussed

Anderson, R.V.

Baillie, D.L.

Beckenbach, K.

Curran, J.

Rutherford, T.A.

Webster, J.M.

Andreev, V.V.

Umnov, A.M.

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

                ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000. №1.   Серия: Плазменная электроника и новые методы ускорения (2), с. 3-7.3UDK 533.9GENERATION OF RELATIVISTIC ELECTRON BUNCHES IN PLASMASYNCHROTRON GYRAC-XFOR HARD X-RAY PRODUCTIONV.V.Andreev, A.M. UmnovPlasma Physics Laboratory, Peoples’ Friendship University of Russia, Moscow, Russia,e-mail: aumnov@sci.pfu.edu.ru– Experiment performed on plasma synchrotron Gyrac-X operating on synchrotron gyromagneticautoresonance (SGA) is described. Gyrac-X is a compact plasma x-ray source in which kinetic energy ofrelativistic electrons obtained under SGA converts into x-ray by falling e-bunches on to a heavy metaltarget. The plasma synchrotron acts in a regime of a magnetic field pulse packet under constant level ofmicrowave power. Experiments and numerical modeling of the process showed that such a regime allowedobtaining dense short lived relativistic electron bunches with average electron energy of 500 keV – 4.5MeV. Parameters of the relativistic electron bunch (energy, density and volume) and dynamics of theelectron bunches can be controlled by varying the parameters of the SGA process. Possibilities of x-rayintensity increase are also discussed.1. IntroductionSynchrotron gyromagnetic autoresonance (SGA) iselectron cyclotron resonance (ECR) in plasma confinedin a simple mirror trap in a magnetic field smoothlygrowing in time. Unlike ECR in case of SGA therelativistic change of the electron mass is compensatedwith the change of the magnetic field in timeB(t)=B0[1+b(t)] (B0=m0cω/e, m0 and e are the rest massand the charge of the electron, ω  - angular frequency ofHF field, b(t) - monotonically growing function of time.As a consequence the resonant condition ceωω ≅  (ωce= eB(t)/m0γc, γ = (1 − v2/c2)-1/2, v  – velocity of theelectron) is maintained automatically. Under SGA theelectron phase ϕ (phase is the angle between the vectorof electric field strength E and the vector of the impulseof the electron p) is being trapped into such an intervalthat average time energy of the electron grows inaccordance with the law of the magnetic field growth:)()( tbtW ≅ , where 1−= γW  – kinetic energy of theelectron in 20cm  units. The maximum value of energyof electrons gained during SGA is limited only byradiation loss. The average electron energy isdetermined by the value of the magnetic field anddoesn't depend on the microwave field strength:[ ]1/)(511)(~ 0 −⋅≅ BtBkeVW .The possibility of such a process was showntheoretically [1] and experimentally [2, 3, 7].Experiments performed on plasma synchrotrons Gyrac-0, Gyrac-D and Gyrac-X as well as simulation of SGAshow that variation of SGA parameters (initial plasmadensity and its dimension, electric field strength,velocity of magnetic field growth) gives a possibility ofobtaining of different plasma objects. In case ofcomparatively small initial radial plasma size andplasma density one can obtain an accelerated bunch ofelectrons. In cases of greater plasma dimension anddensity relativistic plasma formation is generated. Thework is aimed to experimental and numerical study ofrelativistic electron bunches generation and theirtransportation to a heavy metal target for x-rayproduction.2. Experimental deviceGyrac-X is a plasma x-ray source in whichkinetic energy of relativistic electrons obtainedunder SGA converts into x-ray by falling of electronbunches on to a heavy metal target.Fig. 1. Sketch of the Gyrac-X plasmasynchrotronA sketch of Gyrac-X is represented in Fig. 1.The TE111 cavity is exited by microwave at thefrequency 2.4 GHz, 350 W. The static magneticmirror field produced by coils  (L=15 cm, 05.1≅R )satisfies the ECR condition in the midplane of thecavity. Pulse coils produce the pulse magnetic field:μs)500100(  tincr −≅ , G B 500max ≅ . The stainlesswall of the cavity allows penetration of pulsemagnetic field with a small decrease of its strength.Electromagnets used in Gyrac-X experimentsgive it possible to form static magnetic field profilesfor different experimental scenarios: 1) increasingpulse magnetic field [2, 3], 2) reverse pulsemagnetic field [6]. The obtained experimental datashowed that in the first case SGA-trapping is greaterby factor of 2 in comparison with the case of reversemagnetic field. The installation allows running theheating process in the regime of a pack of SGA-4pulses [6] but under constant level of microwavepower.Diagnostic of the relativistic plasma producedwere performed by undertaking analysis of thebremsstrahlung radiation from gas as well as from aW-target (1.5x1.5mm2) placed into relativisticplasma area. X-ray measurement were made by aNAI(Tl) scintillator spectrometer (crystal 25x25mm2, the detection efficiency of photons withenergy 100-300 KeV is no less than 50%) in theregimes of amplitude analysis and registration of x-ray total photon flux intensity. The x-ray detectorsystem was calibrated against a primary standard -γ-source Cs137, Na22 of known intensities. Thecollimated x-ray telescope collects photons from avolume of hot-electron location. The electron bunchradial dimension was defined by bremsstrahlungphoton flux from the target moving along the radius.Diagnostics of produced relativistic plasma wereperformed making analysis of the bremsstruhlungradiation from gas as well as from a W-target placedinto the relativistic plasma location. Figure 2presents oscilloscope traces of such a flux at fixedradius and shows that at the peak of the SGA regimea copious amount of emission is detected, which isobviously radiated by hot electrons colliding withthe target. Determined by this means the value ofthe radius corresponds to the expected relativisticLarmor radius, which only depends on the maximalvalue of electron energy at a given value of thepulse magnetic field strength. Moreover, the energyof most of the energetic individual bremsstrahlungphotons from gas measured during amplitudeanalysis equals the expected value of electronenergy at a given value of the pulse magnetic fieldstrength.Values of density and average energy oftrapped electrons are obtained by integralmeasurement and amplitude analysis from gas.Experiments and numerical modeling of the processshowed that such a regime allowed to obtain denseshort lived electron bunches. Lifetime and densitiesof the electron bunches were determined by initialplasma parameters, microwave electric fieldstrength, velocity of magnetic field growth andrepetition rate of SGA-pulses. The measurement ofintensity of radiation from gas showed that itsmaximum power is equal MeV/s106 4⋅  at rise timeof magnetic field 100 µs, relativistic plasma density- 38 cm104 −⋅ ). The radiation power depends on therise time of pulse magnetic field – a shorter risetime of magnetic field affects the SGA process bybetter trapping condition for the electrons of initialplasma.Fig. 2. Oscillogramms of x-ray flashesfrom the target (upper) and pulsemagnetic field (lower)Obtained experimental and numerical simulationdata showed that time interval during whichrelativistic bunches fell on a target strongly dependson the rate of magnetic field decrease. Variation ofthe repetition rate of SGA-pulses resulted in amaximum value of bremsstruhlung intensity atkHz10 f ≅ .W-target insertion in relativistic plasma locationshowed an increase of radiation intensity but only smallpart of trapped particles falls on it. The intensitystrongly depends on location of the target and its size.Insertion of the target inside the cavity deeper than 2.4cm detunes the resonance.3. Simulation of electron bunches generationand their transportation on to a targetSimulation of SGA was carried out to investigate themain problem of SGA – the problem of trapping ofplasma electrons in a regime of autoresonanceacceleration and to define the influence of SGAparameters and parameters of initial plasma on trappingconditions. Considering the conditions of experiments3D-electrostatic model using particles has been applied[4]. Equations for motion of plasma particles weresolved by means of leap-frog scheme [5]. The numericalcalculations provide information on 3D plasmaevolution, trap losses of particles, energy spectra ofelectrons and ions, and plasma density that are beyondthe reach of both analytical methods and 2D simulation.The aims of the simulation: a) to analyze space particlesdistributions and electron energy spectra dependence oninitial conditions (initial plasma density and volumeoccupied by plasma); b) to determine trappingefficiency of electrons and losses particles from the trap.To solve this problem a 3D electrostatic model withthe use of a CIC scheme is explored. Plasma heatingand confinement is simulated for a typical 2.4 GHzplasma synchrotron.Initially monoenergetic electrons (5 – 50 eV) andions (1eV) homogeneously distributed in space haverandom directions of velocities. We simulated ahydrogen plasma beam of densities of 310 cm10 −axially injected into the cavity and confined in a mirrortrap (mirror ratio R=1.02). Microwave electric fieldstrength is taken 3 kV/cm. The velocity of magneticfield growth in time provides average electron energyincrease 100 keV/µs. To satisfy requirements of aparticle in cell method 10 – 20 particles in a cell are5taken. Because of complexity of the problem underinvestigation, schemes using Cartesian coordinates tosolve equations for particles motion as well as Poissonequation have been used as the most cheapest anddeveloped. Equation of motion for each charged particlein the form of Newton-Lorentz ×+++=cedtdindshfBvEEEp , (1)where p and v are respectively the impulse and thevelocity of a charged particle, e is the electron charge,Ehf  is the microwave electric field strength, Es is theself-consistent plasma electric field, Eind is the inductiveelectric field, B is the superposition of magnetic fieldscreated by static magnetic coils and pulse magneticcoils. Then a dimensionless centered finite differenceapproximation of equation (1) after normalization toωcmo  takes a formnnnnnnbuuguu ×++=∆−−+−+γτ 22/12/12/12/1,(2)where u is an impulse of the electron in cmo  units, gn isthe total dimensionless electric field strength at timemoment n, bn is the normalized magnetic field value,γ  − relativistic factor , τ=ωt is dimensionless time, τ∆is a time step. The equation (1) solved by a second-order leap-frog Boris scheme [5]. For ions anonrelativistic equation is used. This is justified, as theions are not resonant particles.The Poisson equation for periodic conditions(influence of the cavity walls is supposed to beneglected) is solved at each time step by using theBoisvert code. Spatial limitation of plasma is accountedfor by assuming the particles reached the cavity walls tobe lost. Self-consistent electric field values are derivedfrom the obtained potential distribution on the meshwith the use of finite difference derivatives. Electricfield values at points of particle locations are obtainedthrough inverse bilinear interpolation. Magnetic fieldformed by static magnetic coils and pulse magnetic coilsis calculated at grid points. The use of particle in cellmethod provides such an overwhelming spectrum oftime depended plasma parameters and characteristicsthat one has to limit oneself just several of them. In theproposed model the following diagnostics have beenapplied:1. Time dependence of losses for both sorts ofparticles: electrons and ions.2. Evolution of space distributions of electrons andions.3. Time dependence of electron and ion energyspectra.Obtaining this data is enough to analyze collisionlessprocesses taking place in the phenomena of interest.Cross-sections of space distribution of plasmaelectrons after reaching average electron energy W=500keV are presented in Fig. 3. Ions are not shown in thefigure. Calculation was made for initial plasma beam ofradius r0=4 mm, density 3100 cm104−⋅=n , electricfield strength E=3 kV/cm. It is seen from Fig.3 that as aresult of SGA a relativistic electron bunch is produced.Total number of trapped electrons 10103 ⋅=trN .Fig. 3. Cross-sections of spatialdistribution of electrons after SGApulse.Dynamics of such a bunch can be controlled byvariation of magnetic field in time. A routine practice totransport plasma electrons to a target is a magnetic fielddecrease due to short-circuiting both pairs of magneticcoils. Usually time of a magnetic field decrease is equalto one of an increase. In this case the electron bunchtransforms to the electron ring. Interaction of theelectrons with the target lasts long enough but x – raypower is rather low. To increase x – ray power a numberof approaches can be proposed. One of them – proposedin the work – throwing a bunch on a target placed by theside wall cavity or directly on to the cavity's side wall.This is achieved after the short-circuiting one of pulsemagnetic coils when total magnetic field reaches itsmaximum value. Another way is to add one more coilproducing reverse magnetic field. The removal of themagnetic mirror results in appearance of the axialmagnetic gradient in the place where the electron bunchis located. As a result a diamagnetic forcezz BF grad⋅−= µ  (where µ  is the magnetic moment ofthe bunch which is proportional to the kinetic energy ofthe electrons) acts on the bunch. Under action of thediamagnetic force the bunch is pushed towards thecavity's side wall. Simple estimate of an optimal value-4 -2 0 2 4-4-2024accelerated electron bunchtargetY, cmZ, cm-4 -2 0 2 4-4-2024 targetelectronsnontrappedbunchelectronacceleratedY, cmX, cm6of axial gradient showed that for the above mentionedparameters zBgrad  should not exceed 8 G/cm.However this estimate is valid just for static magneticfield in case of a single particle approximation. That iswhy optimal condition for the bunch transportation wasobtained from the analysis of simulation results. Timeof interaction of the bunch with the target andconsequently the power of x-ray depends on the velocityof magnetic field decrease.Fig.4. Time dependence of magnetic fieldB(z,r) profile, r = 2 cmFig.5. Number of electrons has fallen onthe target at optimaltransportation conditionFigure 4 illustrates time dependence of a magneticfield profile for r0=2 cm corresponding to the center ofthe bunch for different time moments. Upper curvecorresponds to the end of SGA stage.For different values of the velocity of the magneticfield decrease one can obtain different times ofinteraction of the bunch with the target At optimaltransportation condition bunch-target interaction timecan be less than 2 ns (Fig. 5).Figure 5 presents a number of electrons falling on atarget at optimal transportation condition. It is seen fromthis figure that interaction of the bunch with the targetlasts during just a few electron revolutions (severalnanoseconds). Taking into account that the bunchcontains 10101 ⋅  electrons at the energy of 0.5 MeV onecan obtain that at conversion rate 10% instantaneouspower of x-ray burst is about 16 kW. Such aninstallation can acts with repetition rate up to 400 Hz.One more way to rise x-ray power is the use ofthe scheme with TE112 cavity (see Fig. 6). In thiscase two electron bunches are produced as a resultof SGA. These bunches are confined in localinternal magnetic mirrors. After short-circuiting oftwo internal coils internal magnetic mirrors areremoved. Then as a result of appearance of themagnetic gradients in the places when electronbunches are located both bunches are pushed to thecentral plane of the system where theysimultaneously face the target and produce x-rayburst (see Fig. 6). X-ray intensity increase by afactor of two takes place in this case.Fig. 6. Scheme of x-ray source with twoelectron bunches. 1 – staticmagnetic field coils; 2 – pulsemagnetic field coils; 3 – electronbunches: 4 – targetTaking into consideration that the achievableelectron energy under SGA is determined by theterminal value of the magnetic field and doesn't dependon the microwave field strength one can obtain electronbunches with energy of tens MeV (such a regime can bepossibly used for synchrotron radiation production).However the density of trapped electrons does dependon microwave field strength [3]. One more parameterinfluencing both the density of electron bunches andrepetition rate of SGA cycles is the velocity of magneticfield growth [6].All things considered, one can estimate feasibleparameters of the electron bunch produced by SGA:average energy of electrons 200 keV – 4.5 MeV,volume 0.25 – 2.0 cm3, density 109 101 - 101 ⋅⋅  cm-3. Asfor the typical x-ray burst it can range between 10 and500 kilowatt during 2.0 – 50 ns. The repetition rate canbe as high as 400 Hz.5. ConclusionObtained experimental and numerical modeling datashow that the most salient feature of SGA is thepossibility of obtaining Gyrac produced plasma orelectron bunches with parameters (average electronenergy, density and volume) which can be varied inwide intervals. The SGA-regime can be used to obtain acontrolled bunch of relativistic electrons due tovariation of magnetic field in time. So the sphere of itsapplications may be very wide. Interest to sources ofradiation on the basis of synchrotron gyromagneticautoresonance may be enhanced by the prospect of7designing a synchrotron radiation source as well as acompact x-ray source for industrial application. Such asource of intense hard x-ray can be used in atomic andnuclear physics, defectoscopy, material processing,medicine and biology.6. References1. K.S.Golovanivsky Autoresonance accelerationof electrons at nonlinear ECR in a magneticfield which is smoothly growing in time //Physica Scripta. 1980, vol. 22, p. 126.2. V.VAndreev., K.S.Golovanivsky. Plasmasynchrotron Gyrac-0 // Sov. Plasma Physics.1985, vol. 11. p. 300.3. V.VAndreev., A.M.Umnov Experiments withrelativistic plasma produced by a microwavedischarge in a time-dependent magnetic field //Physica Scripta. 1991, vol. 43. p. 490.4. R.W.Hockney, J.W.Eastwood Computer.simulation using particles // 1981. McGraw-HillInc.5. A.B.Langdon, F. Lazinsky. Relativistic andelectromagnetic models // Methods in Comput.Phys., Controlled Fusion 1976, vol. 16, p. 347.6. V.VAndreev., A.M.Umnov A.M. Gyrac-D-0Relativistic plasma accumulator and ionaccelerator // Rev. Sci. Instr. 1992, Vol. 63, p.2907.7. V.VAndreev., A.M.Umnov Gyrac-D-0Relativistic plasma and electron bunches inplasma synchrotron of GYRAC // PlasmaSources Sci. Technol., 1999, vol. 8, p. 479.

Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production

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DNA probes for differentiating isolates of the pinewood nematode species complex

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Generation of relativistic electron bunches in plasma synchrotron Gyrac-X for hard x-ray production

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Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

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