The electron cyclotron resonance (ECR) phenom�enon plays a fundamental role in the plasma physics.It has been widely used for plasma heating [1, 2], pro�duction of multicharged ions [3], generation of elec�tromagnetic radiation in different wave bands [4], andin technologies of state�of�the�art microelectronics(e.g., see [5]).
The ECR is a high�efficiency mechanism of thewave–particle interaction when the microwave fieldfrequency coincides with the cyclotron frequency ofan electron in an external magnetic field. The energyacquired by electrons in this case is limited by relativ�istic detuning of the resonant conditions [6].
The method for maintaining the cyclotron reso�nance in an external magnetic with a value increasingin time or in space was proposed in [7, 8]. The ideabehind the method consists in the existence of a phasestability in the motion of a charged particle under con�ditions of a cyclotron (gyromagnetic) resonance in amagnetic field smoothly varying over time. In thismode, should the resonant conditions correspondingto the precise nonrelativistic cyclotron resonance bemet and the increase in the magnetic field value overtime ensures the maintenance of the resonant condi�tions, the mean electron energy increases, followingthe law of the magnetic field rise.
Acquisition of energy by a particle depends on thebehavior of the magnetic field only slightly: the reso�nant conditions are automatically maintained at anarbitrary, but slow increase in the magnetic field; inthis case, the contribution of the induced magnetic
field to the acceleration process is inessential. Themaximum attainable electron energy is limited only bythe synchrotron radiation losses. This mechanism hasbeen called the gyromagnetic autoresonance (GA).Maintenance of these conditions results in generationof long�lived plasmoids [9] with the relativistic elec�tron component, the spatial scale of which is compa�rable to the mean radius of Larmor rotation.
The plasma produced under the GA conditions canbe used in applied research, which is demonstrated byresults published by different authors. A similarapproach can be employed to develop generators ofhard X rays and synchrotron radiation [10–12] andcollective�field ion accelerators [13, 14] and obtainmulticharged ions of heavy elements [3, 15], as well asin a number of other applications.
The purpose of this work is to develop a compactdevice (a plasma accelerator) capable of maintainingthe repetitive mode of gyromagnetic autoresonantacceleration for cold electrons of the injection plasmato energies of a few hundred keV.
In accordance with this purpose, the followingmain tasks have been performed: a complex system hasbeen developed for maintaining the repetitive mode ofaccelerator operation with the possibility of retuning,over wide limits, the parameters determining the elec�tron trapping into the acceleration regime [7, 10]; theranges have been determined for the operating condi�tions of the setup ensuring the availability of the stableacceleration mode; and a set of parameters indicatingthe operation in the GA mode has been experimen�tally determined.
NUCLEAR EXPERIMENTAL TECHNIQUE
A Pulse�Periodic Gyroresonant Plasma AcceleratorV. V. Andreev, A. A. Novitskiy, A. M. Umnov, and D. V. ChuprovPeoples’ Friendship University of Russia, Department of Experimental Physics,
ul. Miklukho�Maklaya 6, Moscow, 117198 RussiaReceived May 31, 2011; in final form, July 8, 2011
Abstract—A plasma electron accelerator based on the gyromagnetic autoresonance effect is described. Elec�trons of the initially cold internal�injection plasma (a classical ECR discharge) are accelerated in the mag�netic field of a magnetic mirror trap under a one�stage effect of the resonant microwave field and an addi�tional pulsed magnetic field. The synchronism in maintaining the resonance conditions is ensured by asmooth increase in the pulsed magnetic field in the course of a microwave pulse. At the moderate values ofthe input microwave power (up to 2.5 kW) and the steady�state and pulsed magnetic fields (each up to 1 kG),it is possible to obtain stable relativistic plasma bunches, in which the energy of the electron components is afew hundred keV. The measured X�ray bremsstrahlung spectra have features characteristic of the energy dis�tribution of photons, and the high�energy tails are recorded in the region of 600–800 keV. The dependencesof the bremsstrahlung characteristics on the experimental conditions—the value of the steady�state magneticfield and the amplitude of the pulsed magnetic field—are investigated. The experimental data are in goodagreement in the quantitative sense with the results of the computer simulation and with the earlier studies.
DOI: 10.1134/S0020441212020121
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DESCRIPTION OF THE EXPERIMENTAL SETUP AND THE DIAGNOSTIC TECHNIQUES
The experimental investigations were conductedon the setup, the layout of which is shown in Fig. 1.Physically, the experimental setup is an axially sym�metrical system, in which microwave cavity 1 andpulsed magnetic field coils 3 combined in a single unitare disposed in the interpolar space of electromagnet 2that creates a steady�state magnetic field.
The steady�state magnetic field with the classicalprofile of the magnetic mirror trap is produced by theWeiss�type electromagnet. To carry out experiments, acircuit balancing the electric current in the indepen�dently fed coils has been included in the setup. TheN5752F power sources (Agilent, 600 V, 1.3 A, GPIB)operate in the current stabilization mode and arecapable of balancing currents in the coils under soft�ware control. This helps us to maintain the value of thesteady�state magnetic field in the middle plane of thecavity at a level required by the particular experimentalconditions, or to smoothly vary it.
The magnetic field strength is measured by anSS�94A2D Hall�effect sensor (Honeywell) with a sen�sitivity of 1 mV/G, which allows the taking of mea�surements in the range of up to 2500 G with an accu�racy of 1.5% of the range. The experimentallyobtained 3D distribution of the steady�state magneticfield induction is shown in Fig. 2a. At equal currents inthe coils, it has a magnetic mirror configuration (R =1.6 mm and L = 120 mm), which ensures long�termconfinement of plasma bunches in the working vol�ume of the cavity.
Under the resonant conditions within the operat�ing volume of the cavity, when the cyclotron frequencyωсе for the electron rest mass coincides with the pumpmode frequency ω0, the trap is filled with the injectionplasma upon a breakdown. The characteristics of thisplasma are strongly dependent on parameter
, where ωc0 = corresponds tothe induction of the steady�state magnetic field at thecenter of the cavity. At β = 1, the trap is characterizedby the resonant induction values of the axial magneticfield of 875 and 1450 G at the center and the end wallsof the cavity, respectively (Fig. 2a).
Generation of the magnetic field increasing in timewas effected by discharging a capacitive storage via twopulsed coils (see Fig. 1), which were connected inseries and placed in alignment with the coils of thesteady�state magnetic field and the cavity. In the caseof two coaxial identical coils with a small cross sectionof their windings, equal values of the currents flowingin the same direction, and a constant current density,the geometrical efficiency is a function of the relativesize of the system [16, 17]. The geometrical dimen�sions of the pulsed coils were selected from the linearsizes of the region within which the magnetic fieldstrength had to be increased over time with a predeter�mined degree of homogeneity and the characteristictime scale.
According to [17], the spatial inhomogeneity of thefield on a length of 50 mm is ~1% at the selectedgeometry and width of the winding. Figure 2b presentsthe calculated superposition of the Z components ofthe measured steady�state and calculated pulsed fieldsat a pulsed field amplitude of 1000 G. The measure�ments of the pulsed magnetic field at the referencepoints have demonstrated the insignificant disagree�ment with the calculation.
A periodic pulse current generator (PCG) has beendeveloped and produced for generation of the pulsedmagnetic field. The use of the low�resistance pulsedcoils and the capacitive storage ensured the periodicdischarge mode with attenuation factor γ = 0.01.
The commutating angle is the characteristicparameter of switches operating in circuits with theperiodic discharge of the storage. The instant when thecircuit is closed and the storage starts discharging is
/0 0cβ = ω ω / 0(0,0) ( )eB m c
A
A
A–A
2
3 1 3
2
Mic
row
ave
dia
gno
stic
s
Monochromator,CCD cameraMicrowave
power input
Х�ray camera,photodetector
Gasinleakage
Pumping
Target
NaI(Tl) detectorSi(Li) detector.
Fig. 1. Diagram of the setup: (1) microwave cavity, (2) electromagnet, and (3) pulsed magnetic field coils.
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considered to be the zero time, and the phase of thecurrent curve at the instant of interruption of the cir�cuit or forced switching of its operating mode is char�acterized by commutating angle ϕc. At commutatingangles in the range of (0, π/2), partial discharge of thestorage occurs. The commutating angle of π/2 corre�sponds to the total energy transfer to the inductive load(the dissipation is ignored).
To ensure high�efficiency periodic operation of theaccelerator, it is important that the inverse recupera�tion of the electromagnet energy into the storage beimplemented at commutating angles of <π/2 [16].Such an approach helps to increase the repetition rateof the current pulses without increasing the power ofthe rectifier that charges the capacitor. In practice, thisproblem is solved by changing the poles of the induc�tive load at the instant of commutation, so that the emfof the induction produced upon interrupting the cur�rent is applied to the capacitive storage in polarity cor�responding to its initial charging. The diagrams ofvoltage across capacitor uC and current in the inductiveload iL corresponding to this process are shown inFig. 3a. If we ignore the dissipative loss, we see that, atthe instant of commutation, current phase ϕc changesstepwise to value π–ϕc, and the energy stored in thepulsed coils is repeatedly converted into the charge ofthe capacitive storage, charging it to the initial voltageby moment 2ϕc.
The circuit diagram of the commutator that imple�ments this principle using switches based on IGBTtransistors is shown in Fig. 3b. The functions of theswitches that open and close the storage discharge cir�cuit are performed by transistors Q1 and Q2(CM600HA�24F, Mitsubishi Electric). Diodes D1 andD2 (RM400HA�34S, Mitsubishi Electric) ensure the
flow of the recuperated current after the main switchesopen and the induction emf appears with the polarityindicated in Fig. 3b as a sign in the brackets. Versatiledrivers of the IGBT transistors (SKHI 10/12, Semik�ron; not shown in the figure) are used to control thevoltage applied to the transistor gates. An industrialcomputer based on the PXI bus fulfills the functions ofthe synchronizing device. The time intervals are spec�ified with the aid of 32�bit counters–timers (NI�PXI�6022, National Instruments). At off�duty factor Q =20–30, the natural convection mode is sufficient forholding the main elements of the loop within the limitsof the operating (calculated) parameters.
For experimental investigations, the amplitude andrise time of the magnetic induction inside the cavityare the most important characteristics of the pulsedmagnetic field. The small thickness of the chamberwalls with respect to the skin�layer thickness are theconditions for penetration of the slowly changingmagnetic field into a hollow conductor. The thicknessof the cavity walls in the site of the pulsed magneticfield coils is 1 mm. The measurements have shownthat the rate of the magnetic field rise is slightlydelayed with respect to the current in the inductor,which is the evidence that skinning results in onlyminor attenuation of the magnetic field.
The vacuum cavity is a split metal cylinder withdemountable vacuum�tight end covers. In the cavity,there are pistons used to tune the cavity to the operat�ing frequency of the microwave generator. The neces�sary increase in the rigidity of the cavity’s volume andits resistance to deformation are ensured by a ring�shaped hard rib in the middle plane of the cavity. Thehard rib has vacuum ports with Wilson�type seals,which are used to input microwave power, connect
2400
2000
1600
1200
800
–40 –20 0 2040
–40
–20
020
40
(a)
R, m
m
Z, mm
B, G
2400
2000
1600
1200
800
–40 –20 0 2040
–40
–20
020
40
(b)
R, m
m
Z, mm
B, G
Fig. 2. Magnetic field structure: (a) experimental 3D diagram of the axial component of the steady�state magnetic field and(b) theoretical 3D diagram of the axial component of the superposition field created by the stationary and pulsed coils.
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diagnostic elements, the gas inleak, and monitor thevacuum directly in the working volume of the setup.The background pressure in the working volume of thecavity is <10–6 Torr. The gas was inleaked via a piezo�electric valve, and argon was used as a plasma�produc�ing gas. The operating pressure was varied within thelimits of 10–5–10–4 Torr.
The cavity was excited at a fundamental modeТЕ111 by a magnetron generator with frequency f =2450 MHz. Owing to the built�in modulator, the gen�erator operated in a pulse mode with a duration of 50–1000 μs and a pause of 1–100 ms, which ensured thespectrum of durations and off�duty factors corre�sponding the timing characteristics of the PCG. Thewaveguide section with a ferrite circulator, attenuator,and a matched load allowed the decreasing power levelto be regulated within the limits of 500–5000 W withfluctuations of ≤2.2%. The measurements of theamplitude–frequency response (AFR) showed that Qfactor of the cavity was Q = 720 at SWR = 2.5.
The device as a unit functions in the pulse�periodicmode. The oscillograms of the microwave and mag�netic�field pulses characterizing the script of theexperiment are presented in Fig. 4. In the initial phaseА, breakdown of the gas happens under the ECR con�ditions, and the cavity is filled with the injectionplasma; in phase В, plasma electrons are trapped andaccelerated under the GA conditions; and phase С isthe phase of accelerated electron confinement in themagnetic field of the magnetic mirror configuration.
Based on the theoretical requirements for thedimensionless values of the rate of magnetic field riseα and amplitude of the electric microwave fieldstrength g0 [7]
( )1max
0
1 ;B
tB
−
⎛ ⎞α = − ω⎜ ⎟
⎝ ⎠
particle trapping into the GA mode is possible if thefollowing criterion is satisfied:
α ≤ 1.19g4/3, (1)
which ensures acceleration of trapped electrons toenergies
(2)
The ranges of these parameters for the developedexperimental setup are: α = 4 × 10–8–1.3 × 10–7 andg0 = 1.5 × 10–3–1 × 10–2. They allow us to experimen�tally investigate the degree of influence of theseparameters on the timing and spatial characteristics ofthe electron trapping into the GA mode.
The main objective of our experiments is to deter�mine the relationships between the maximum energyof electrons accelerated under the GA and a set of theoperating parameters—the initial magnetic field, theamplitude of the pulsed magnetic field, and the rate ofits rise. This information can be obtained by analyzingthe spectrum and intensity of bremsstrahlung pro�duced during interaction between accelerated elec�trons with energies of a few hundred keV and the Cou�lomb field of an atomic nucleus or electrons of theinner shells in plasma�producing gas atoms. The loca�tion of the diagnostic facilities is shown in the sche�matic diagram of the experimental setup (Fig. 1).
Radiation was detected in a direction orthogonal tothe vector of the magnetic field strength in the centralcross section. An X�ray detector unit based on a NaI(Tl)scintillator with dimensions of 40 × 40 mm was used.The detector was equipped with a lead shield and acollimating system with a set of lead apertures (from 1to 3 mm). Depending on the requirements of anexperiment (radiometry or spectrometry), the signals
00
,eEgm c
=
ω
20
0
1 .BW m cB
⎛ ⎞= −⎜ ⎟⎝ ⎠
uC
iL
ωt
ωt
ϕc 2ϕc
ϕc π/2 π–ϕc
Q1
Q2
C
(a) (b)
L
(+)
(–)
–
+ D1
D2
Fig. 3. (a) Diagrams of the currents and voltages and (b) circuit diagram of the pulsed current generator.
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from the detection unit were recorded by an oscillo�scope or were fed to an multichannel analyzer (1024channels) integrated with a personal computer, forsubsequent processing. The main difficulty encoun�tered in carrying out the experiment was the necessityto avoid overloading of the data acquisition channelunder conditions of a high quantum yield. The colli�mating system with a small solid angle of detection wasused to optimize the throughput of the detector andthe spectrometric electronics. Radiation from theregion of interaction was ejected through a berylliumwindow 0.47 mm thick. Taking into account the colli�mating system, the solid angle of view ensured radia�tion detection from a volume of ~9 cm3.
The spectrometer was calibrated in the requiredenergy range. The linearity of the response of the spec�trometric and radiometric detection units was checkedby calibrating them using reference radiation sources(Am�241, Cs�137) in the region of interest in the radi�ation spectrum. The main parameters of the spec�trometer—the energy scale division, the energy reso�lution, and the detection efficiency—were deter�mined. Thus, the energy resolution and the signal�to�background ratio for the 662�keV peak were
and δ = 7.1, respectively.
The calibration measurements have shown that thedetector is capable of detecting γ rays with energiesranging from 50 keV to 3 MeV. The basic error in theenergy region of interest (~500 keV) is 10% or less.The measured efficiency, energy resolution, and sig�nal�to�background ratio have made it possible, takinginto account the radiation absorption in the spectro�metric channel, to introduce corrections in therecorded spectra and obtain thereby the true shape ofthe X�ray spectrum generated by the plasma.
It should be noted that the radiation intensity of thegas target is related to the beam current and its local�ization in space by the linear dependence [18], whichallows us to judge the degree of trapping of injectionplasma particles into the acceleration regime. There�fore, to raise the reliability of measurements, X raysemitted only by the gas�target have been detected,since this excludes spectrum distortions that canappear in detection of radiation produced in interac�tions with the chamber walls by particles either non�trapped or lost during acceleration. The characteristicradiation from the gas target with energies of a few keVcould not affect results of these measurements, since,in this energy range, the sensitivity of the detectingsystem is low.
To determine the geometric dimensions of gener�ated plasma bunches and the timing characteristics ofparticle transport in a radial direction, we measuredradiation produced in interaction of the acceleratedbunch with a small (3.5 × 1.5 mm) solid�state Taprobe–target and the current in the probe circuit. Thetarget, which could freely move along the cavity radius
( ) 9%R E γ =
and rotate about the axis of the rod (Fig. 1), was placedin the region of hot electron component localization.
In the spectrometric measurements, the acquisi�tion time for each spectrogram was 1024 s at an accel�erator off�duty factor of 35 ms and a microwave pulseduration of 1 ms. Therefore, the recorded spectro�grams corresponded to the signal averaged over ~3 ×104 pulses of the setup.
NUMERICAL SIMULATION OF THE PLASMA UNDER THE GYROMAGNETIC
AUTORESONANCE CONDITIONS
Prior to carrying out the experiment, the behaviorof the plasma and its main parameters under the GAconditions was investigated by three�dimensionalnumerical simulation using the particles�in�cellmethod [11, 19–21] in view of the electrostatic inter�actions. The self�consistent magnetic field of theplasma has not been included in the model, since theparameters under investigation (the plasma densityand the average energy of the electron component) aresuch that it affects the GA process only slightly. Theparameters and characteristics of the experimentalsetup described above (the size, the spatial and tempo�ral configurations of the magnetic and electric fields,the injection plasma parameters, etc.) were all takeninto account in the model.
The key parameters of the numerical model (thegeometrical dimensions of the vacuum chamber, themagnetic field configuration, the mode of microwaveoscillations, and the amplitude of the microwave fieldstrength) were selected in accordance with the param�eters of the experimental setup. The electric micro�wave field was calculated under the assumption thatTE111 oscillations were settled in the vacuum chamber.
1
2
A B C
Fig. 4. Signals from the detector (1) of the incident micro�wave and (2) the pulsed magnetic field in different phases(A–C) of the experiment.
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At the initial stage of the GA process, the topology ofthe ECR surface was varied by changing parameter .
The computational experiment fully complied withthe script of the full�scale experiment, except for theduration of the GA process. The rise time of the mag�netic field was assumed to be 1–5 μs, which corre�sponded to the trapping criterion (1). The duration ofthe physics experiment was 300–600 μs.
The initial state of the plasma was calculated for thepredetermined initial parameters of the experimentunder the ECR conditions. The simulation of the ECRplasma was performed until its parameters reachedtheir steady states. The density of the fully ionized
quasi�neutral ECR plasma was cm–3, and thetotal number of model particles was 240000. The nextstage of simulation implied the application of a pulsedfield, which increased according to the sine law (theGA process) to 1000 G and then decreased accordingto the linear law. The ionization and recombinationprocesses were ignored.
The Poisson equation was solved on astandard Cartesian grid with 64 × 64 × 64 nodes usingthe fast Fourier transform method. The self�matched
plasma electric field was calculated at thenodes using the difference derivatives of potential
, where are the numbers of nodes in theX, Y, and Z directions, respectively.
The electron motion equation presented in thefinal differential form
(3)
was solved according to the scheme proposed in [20].In Eq. (3), is the electron momentum in terms of units; is the dimensionless time step; τ = ωt is the
dimensionless time; is the dimensionless
electric field, where is the sum ofthe strengths of the microwave field, the induced elec�tric field, and the self�consistent electric field of the
plasma; is the dimensionless induction of
the magnetic field, where is the sum ofthe steady�state and pulsed magnetic fields producedby the coil systems; ; and is the relativ�istic factor. The superscript in Eq. (3) is the time stepnumber in integrating the motion equation. The ions(hydrogen) are neither magnetized nor relativistic.
The developed model has made it possible to inves�tigate the evolution of the main plasma parameters inthe GA process, determine the rate of particle lossesfrom the plasma, and study the dependence of theelectron energy spectra on the initial conditions andparameters of the numerical experiment.
Analysis of the results of the computational experi�ment has demonstrated their qualitative and, in most
β
910en =
4ΔΦ = − πρ
E = −∇Φ
�
( , , )i j kΦ , ,i j k
1 1 1 12 2 2 2
2
n n n n
n n
n
u u u ug b
+ − + −
− += + ×
Δτ γ
� � � �
�
�
u�
0m cΔτ
0ng E B=
�
�
hf s iE E E E= + +
� � � �
0n nb B B=
� �
st impB B B= +
� � �
0 0B m c e= ω γ
cases, quantitative agreement with the results of thefull�scale experiment. Figure 5 presents the character�istic profile of the spatial distribution of electrons andtheir energy spectrum, obtained in the course of theincrease in the pulsed magnetic field to 1000 G at astart magnetic�field value at the trap center of 866 Gand a magnetic field rise time of 5 μs (electric micro�wave field strength Е = 1 kV/cm).
The trapped electrons constitute a bunch rotatingwith average Larmor radius cm and an aver�age energy of 520 keV in the magnetic field with aninduction of 1900 G (from now on, the field corre�sponds to the value at the geometrical center of thetrap). The nontrapped electrons account for ~15–20% of the total quantity. The time dependence of therate of electron and ion losses ΔNloss/Δt is presented inFig. 6.
From Fig. 6, it follows that the initial GA stage ischaracterized by intense electron losses at the cavitywalls (curve 1). This can be attributed to the increasedradii of cyclotron rotation of electrons located near thechamber walls. As a result, the generation of an excesspositive charge leads to an increase in the ion loss rate(curve 2).
Thereafter, the rates of electron and ion lossesdecrease, the average values of the electron and ionconcentrations are equalized, and the plasmoid on thewhole remains electrically neutral.
RESULTS AND THEIR DISCUSSION
The preliminary laboratory tests of the acceleratorwere performed under the following conditions: at apressure ranging from 10–5 to 10–4 Torr, and a micro�wave power varying in the range of 1.5–2.5 kW. Themagnetic field detuning β, the pulsed magnetic fieldamplitude, and the rate of its rise were also varied.
In the course of the experiment, the spectral andintegral bremsstrahlung characteristics were measuredand investigated. The results allowed us to determinethe ultimate energy of the injection plasma electronsaccelerated in the GA mode, as a function of the oper�ating parameters. In compliance with the limitingvalue of the pulsed magnetic field induction of~1000 G and the resonant value of 875 G, the energyof electrons accelerated under the GA is expected,according to Eq. (2), to be 580 keV. The indicationthat the GA mode has been attained is the detection ofhard bremsstrahlung with the photon energies corre�sponding to the calculation. This energy is consider�ably higher than the energy obtained in implementa�tion of possible competing effects—the classical ECRheating followed by the adiabatic compression phase[22].
The oscillograms recorded in the diagnostic chan�nels are presented in Fig. 7 to confirm the implemen�tation of the GA mode at the experimental setup. Themicrowave pump pulse (curve 1) caused the break�
1.95Lr =
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down of the gas and the development of a discharge inthe ECR mode. The initial phase of the discharge wasindicated by a flash of light emitted in the visible andnear UV spectrum regions and detected by the photo�multiplier tube (PMT, curve 3). The magnetic fieldpulse (curve 2 with a scale of 1 G/mV) was initiated atthe instant when the ECR discharge plasma hadalready been produced. The magnetic field stoppedincreasing simultaneously with the end of the micro�wave pump pulse. The presence of the hot electroncomponent in the plasma is revealed by the detectionof hard bremsstrahlung from the gas (curve 4 with ascale of 0.16 keV/mV). At the same time, the currentof the probe–target placed in the discharge was mea�sured to localize the spatial region of the relativisticplasma bunch (curve 5).
According to the recorded oscillograms, theparameters of the injection plasma are constant (curve 3)by the start of the GA mode. X�ray radiation detectedin the acceleration process at a 1000�G amplitude ofthe pulsed field (curve 4) contains X�ray photons thatattain relativistic energies corresponding to the valuesof ~500–600 keV calculated according to Eq. (2). Thisis the evidence that the mechanism of GA accelerationof injection plasma electrons has been implemented.
Plasma confinement is also accompanied by thegeneration of X rays with energies slightly lower thanthe above�mentioned value and the characteristic life�time of ~10 ms, which can be attributed to the decom�pression in the magnetic field decreasing with time.Such a long time of detection of X rays generated bythe interaction between fast electrons and atoms of theplasma�producing gas indicates that the GA accelera�tion cycle in the working volume results in the forma�tion of a stable spatially localized electron bunch withan energy of a few hundred keV, which is confined inthe classical magnetic mirror trap. The resultsobtained by processing the oscillograms (Fig. 7b) haveshown that the integral power of the bremsstrahlungburst reaches its maximum by the end of the accelera�tion cycle. This is the indication that a large number ofelectrons have been trapped in the GA mode.
The Larmor radius of a 500�keV electron in themagnetic field with an induction of ~1700 G is 1.7 cmand, at an induction of 875 G, 2.2 cm in view of thefact that the energy decreases from the measured (cal�culated) value to 250 keV as a result of decompression.The inhomogeneity of the injection plasma and thelarge linear dimensions of the spatial region of trap�ping cause the transverse linear dimensions of theplasma bunch being produced to exceed the Larmorradius of electrons with the respective energy. This fact
100
50
0
–2
–2
100
150
200
200 500 700Energy, keV
(b)
1
2
ΔN/ΔW
(a)
–3–4 10–1 432
–3
–4
1
0
–1
4
3
2
X, cm
Y,
cm
300 400 600
250
300
350
400
Fig. 5. (a) (X, Y) profile of the spatial plasma distribution(the solid circles denote trapped electrons and the opencircles denote ions); the electron rotation direction isshown with the arrow; (b) energy spectrum (1) of trappedand (2) nontrapped electrons.
8.75
50
7.500
100
150
200
10.00 11.25 12.50t, μs
1
2
ΔNloss/Δt, arb. units
Fig. 6. Rates of the electron (a solid line) and ion (a dashedline) losses in the GA process (the time from the start of theGA process is laid as the abscissa).
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has been experimentally confirmed by the measure�ments using a probe–target (the current measurementmode), capable of moving along the radius of the cav�ity, and a bremsstrahlung detector with a varying solidangle of view.
When the probe–target moved from the wall deepinto the cavity toward its center so that the unit vectorof the target plane was oriented perpendicularly to themagnetic field direction, the following characteristicswere found out: the positive current on the target was
(а) (b)
1
2
3
1
2
5
4
Fig. 7. Time dependences of the processes in the GA mode: (1) microwave pulse, (2) magnetic field pulse, (3) PMT signal, max�imum sensitivity is in the spectral region of 350–420 nm), and (4) signal from the X�ray detector, and (5) current signal from theprobe–target.
300
200
100
0 600400200 800Energy, keV
Events
1
2
3
Fig. 8. Bremsstrahlung spectrum from the gas target for different amplitudes of the pulsed magnetic field: (1) 600, (2) 800, and(3) 1000 G; β = 1; the pressure in the working volume is 10–5 Torr; and the microwave power is 2500 W.
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measured in the region near the wall during the GA,and, as the probe moved along the radius to a depth of20 mm from the cavity axis, the negative current wasdetected, the occurrence of which correlated with thedetected bremsstrahlung (Fig. 7b).
In a qualitative sense, these dependences coincideboth with the results of the numerical simulation(Fig. 5a) and with the above estimate for the transversedimensions of the generated bunches. Therefore, atthe initial instant of time, the region of GA interactionis a source of charged particle fluxes in the radial direc�tion.
The generated plasma can be conditionally dividedinto two regions in the transverse direction. The non�compensated ion flux is observed in the region close tothe cavity surface, and a stable bunch of relativisticelectrons is concentrated at the center. In addition, thegenerated plasmoid also contains the other compo�nents—populations of cold electrons and ions; how�ever, the diagnostic facilities used in our study areinadequate for carrying out their rigorous experimen�tal investigation.
Taking into account that the cavity radius is 45 mm,we can conclude that, in the course of acceleration,the outer layers of the injection plasma lose their elec�trons on the walls as a result of the GA. Ions from theselayers must also be carried by the ambipolar field to thewalls, so that the plasma bunch will contain only aportion of particles initially stored in the plasma. Sincethe effective cross section of momentum transferdecreases with increasing energy and the time betweencollisions increases, the generated bunch can be con�fined for a long time in the magnetic field of the mag�netic mirror trap in the absence of radical instabilities.
Immersion of the flat target into the region of local�ization of the hot electron component caused thedetected radiation intensity to abruptly increase. Thisallowed us to determine the characteristic thickness(in the radial direction) of generated bunches, whichappeared to be 0.3–0.4 cm. As shown by the measure�ments, the intensity of bremsstrahlung from the targetdepends on the target orientation. A turn of the targetplane through 90° to the position where the unit vectorof the target is aligned with the lines of the magneticfield results in a decrease of 80% in the integral power,which approximately corresponds to the ratio of thetarget’s effective areas in the two above�mentioneddirections. This confirms the result of the numericalsimulation, which corresponds mainly to the azi�muthal character of motion of the acceleratedbunches (Fig. 5a).
As a result, the characteristics of detected X raysmeasured by moving the probe and changing its orien�tation, in combination with the results of the compu�tational experiment, have made it possible to obtainthe simplified notion of the spatial characteristics ofthe bunch and its motion. The complex motion of thebunch under these conditions can be presented asrotation of the driving center of the bunch around its
symmetry axis. In this case, the characteristic dimen�sions of the bunch are determined by the radius of azi�muthal Larmor rotation of relativistic electrons andthe radial width of the trapping region for injectionelectrons.
By contrast to the ECR conditions, the plasmaproduced under the GA conditions is characterized bya significant increase in the drift velocity in the azi�muthal direction, which is associated with the inho�mogeneity of the magnetic field and with the radiallydirected ambipolar electric field. A growth of the elec�tron energy in the GA process causes the bounce oscil�lations of electrons to decrease in amplitude, which insuccession leads to an increase in the plasma density(axial compression). As a result, the plasma densityincreases in comparison with the density of the initialplasma, though some particles are lost.
Even if we try to describe the plasma bunch motionmore carefully, it is nevertheless useless to take into
150
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400 600 800Energy, keV
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Background level
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600
Energy, keV
600
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400
600 800 1000Amplitude of the pulsed
magnetic field, G
Fig. 9. (a) High�energy tails of the X�ray spectra and (b)dependence of the ultimate energy in the bremsstrahlungspectrum on the amplitude of the pulsed magnetic field.
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account the transverse diffusion of electrons in themagnetic field, which occurs by collisions. In ourexperiment, the electron range and the respectiverelaxation times are long in comparison with the char�acteristic spatial and time scales. Therefore, whendescribing the character of the plasma bunch motion,we may ignore collisions of particles and take intoaccount only their collective interaction via the self�consistent fields produced during generation and con�finement of bunches.
To determine the maximum attainable energies ofelectrons accelerated in the GA mode versus theparameters of the experiment (the rate of the magneticfield rise, the amplitude of the pulsed magnetic field,and detuning of the start magnetic field), bremsstrahl�ung spectra from the gas target were recorded.
The radiation spectra recorded and processed inview of the instrumental function of the γ spectrometer(the quantum and energy efficiencies, the signal�to�background ratio, and the absorption in the exit beryl�lium window and the electronic section), are pre�sented in Fig. 8 under identical initial conditions fordifferent values of the pulsed magnetic field ampli�tude. For the above dependences, the start magneticfield was 875 G, which corresponded to detuningβ = 1; the microwave power was 2.5 kW; and the pres�sure in the operating volume was 10–5 Torr.
The dependences presented in Fig. 8 clearly reflectthe fact that the maximum energy increases with an
increase in the amplitude of the pulsed field. This factis in agreement with the well�known statement thatthe effective energy of bremsstrahlung photons is equalto one�half the maximum energy (Еmax) of decelerat�ing electrons at Еmax < 10 MeV. Detected radiation isproduced only by the interaction of accelerated elec�trons with the gas atoms, since its spectrum does notcomprise characteristic radiation lines of the chambermaterials, which would inevitably appear in the inter�action of accelerated electrons with the chamber walls.
To obtain the dependence of the attainable energylevel on the amplitude of the pulsed magnetic field, theexperimental spectra in the region of their high�energy“tails” were fitted by smooth curves with due accountof the signal�to�background ratio (Fig. 9a). Theobtained dependence coincides with the results of thenumerical simulation and the basic statements of thesimplified theoretical representation of the GA pro�cess (2) if the particle trapping conditions are satisfied.This means that the value of the gained energy (withdue account of the measurement error) linearlydepends on the maximum induction of the pulsedmagnetic field (Fig. 9b).
Figure 10 presents the spectrograms obtained at aconstant value of the pulsed magnetic field amplitude(1000 G) for different values of the initial magneticfield detuning. Similar processing of the high�energytails in the spectrograms (Fig. 11a) shows that the
250
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0 600400200 800Energy, keV
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3
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Fig. 10. Bremsstrahlung spectrum from the gas target for different start magnetic fields: (1) β = 0.98, (2) 1.06, and (3) 1.18;Bpulse = 1000 G; the pressure in the operating volume is 10–5 Torr; and the microwave power is 2500 W.
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maximum attainable energy is practically independentof β within the measurement accuracy (Fig. 11b).
At the same time, the preliminary estimates of theintegral characteristics of radiation indicate that,should the trapping conditions (1) be satisfied, thedetuning of the initial magnetic field affects the num�ber of trapped particles, which results from theincrease in the concentration of the injected plasma ata minor change in the temperature of the cold compo�nent [4].
CONCLUSIONS
The experimental investigations are convincingevidence that the GA acceleration mode has beenimplemented in the developed accelerator. The pre�cise dependences of the energy of electrons acceler�ated to relativistic energies on the operating parame�ters of the accelerator have been experimentallyobtained.
It has been established that the achieved level ofaccelerated electron energies is governed by the maxi�mal value of the pulsed magnetic field in the GA accel�eration process. Detuning of the starting magnetic
fields in the injection regime determines the degree ofparticle trapping, but does not affect the level ofattainable electron energies. The obtained depen�dences are in good quantitative agreement with theresults of calculations in view of the constructionalfeatures of the developed accelerator.
The character of the timing dependences ofrecorded signals and their comparison with the resultsof the numerical simulation have allowed us to quali�tatively describe the formation of generated bunchesand to reveal the quantitative agreement between theexperimentally obtained dependences and the resultsof calculations. The simulated values of the maximumenergy acquired by electrons comply with the experi�mental results with an accuracy of 5% or better. This isevidence of the high reliability and adequacy of thedeveloped numerical model, which allows one to pre�dict the obtaining of plasmas with the parametersspecified beforehand.
Based on the described principle, it is possible todevelop facilities for generating relativistic plasmabunches with the energy of the electron component onthe order of a few MeV and with a long time of theirconfinement (a few hundreds milliseconds) in themagnetic mirror trap. Based on this principle, concep�tual models have been proposed for development ofthe particle accelerator [23, 24], generators of radia�tion [12, 14], and sources of multicharged ions [3].
ACKNOWLEDGMENTS
We are grateful to the participants of the joint sem�inar of the Department of Experimental Physics at thePeoples’ Friendship University of Russia, as well asV.I. Ilgisonis and A.A. Skovoroda, the employees atthe National Research Centre “Kurchatov Institute,”for the fruitful discussions and critical remarks duringpreparation of this paper.
This work was supported by the Federal Target Pro�gram “Scientific and Scientific�Pedagogical Person�nel of Innovative Russia” in 2009–2013 (State Con�tract no. P23�13).
REFERENCES
1. Jaeger, F., Lichtenberg, A.J., and Lieberman, M.A.,Plasma Phys., 1972, vol. 14, p. 1073–1100.
5. Balmashnov, A.A., Golovanivsky, K.S., Omelja�novsky, E.M., et al., Semicond. Sci. Technol., 1990,vol. 5, p. 242.
150
100
50
0
(a)
(b)
400 500 600 700 800Energy, keV
Events
Background level
β = 1.181.06
0.98
Energy, keV600
500
400
300
1.0 1.1 1.2 β
Fig. 11. (a) High�energy tails in the X�ray spectra and (b)dependence of the ultimate energy in the bremsstrahlungspectrum on the value of the start magnetic field.
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≈0
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ANDREEV et al.
6. Roberts, C.S. and Buchsbaum, S.J., Phys. Rev. A.,1964, vol. 135, no. 2, p. 381.
7. Golovanivsky, K.S., Phys. Scripta, 1980, vol. 22, p. 126.8. Andreev, V.V. and Golovanivsky, K.S., Phys. Lett. A,
1984, vol. 100, p. 357.9. Andreev, V.V. and Golovanivsky, K.S., Fiz. Plazmy,
1985, vol. 11, no. 3, p. 300.10. Andreev, V.V. and Umnov, A.M., Phys. Scripta, 1991,
vol. 43, no. 5, p. 490.11. Andreev, V.V. and Umnov, A.M., Plasma Sources Sci.
14. Ishibashi, T., Hattori, T., Hayashizaki, N., et al., Proc.3rd Ann. Meeting of Particle Accelerator Society of Japanand 31st Linear Accelerator Meeting in Japan, Sendai,2006, p. 568.
15. Andreev, V.V., Umnov, A.M., and Apracsin, A.V., Rev.Sci. Instrum., 1992, vol. 63, no. 4, p. 2907.
18. Kuznetsov, L.I., Prikhod’ko, V.G., and Yarygin, V.N.,Instrum. Exp. Tech., 2000, vol. 43, no. 1, pp. 106–109.
19. Hockney, R. and Eastwood, J., Computer SimulationUsing Particle, Bristol: Hilger, 1988.
20. Birdsall, C.K. and Langdon, A.B., Plasma Physics viaComputer Simulation, Philadelphia: IOP, 1995, p. 305.
21. Sigov, Yu.S., Vychislitel’nyi eksperiment: Most mezhduproshlym i budushchim fiziki plazmy (Numerical Exper�iment: Bridge between Past and Future of Plasma Phys�ics), Moscow: Fizmatlit, 2001, p. 223.
22. Alexeff, I., Harris, J.G., and Murphy, C., Phys. Rev.Lett., 1974, vol. 32, no. 19, p. 1035.
