generation of nanosecond neutron pulses in vacuum accelerating tubes

ISSN 1063�7842, Technical Physics, 2014, Vol. 59, No. 6, pp. 904–910. © Pleiades Publishing, Ltd., 2014.Original Russian Text © A.N. Didenko, A.E. Shikanov, V.I. Rashchikov, V.I. Ryzhkov, V.L. Shatokhin, 2014, published in Zhurnal Tekhnicheskoi Fiziki, 2014, Vol. 84, No. 6,pp. 119–125.

904

INTRODUCTION

At present, it is possible to outline a number ofimportant trends in the applied nuclear physics, inwhich emitters of neutron pulses with a short duration(from units to hundreds of nanoseconds), based onaccelerating tubes (ATs), are required. These trendsinclude detection of explosives, drugs, and fissilematerials, neutron radiography of fast processes on thebasis of portable equipment, time�of�flight neutronspectrometry for elemental analysis, and testing ofdetectors of neutrons emitted in thermonuclear reac�tions during short time intervals (~10–9 s) [1–5].

Implementation of nanosecond regimes of neutrongeneration is due to the need for the formation ofextremely short bunches of accelerated deuteronsbombarding an AT target. In this work, we considerthe generation of neutron fields with similar timestructure using vacuum neutron tubes (VNTs). Theinvestigation of the generation of short neutron pulsesusing VNTs and the development of appropriate tech�nical facilities, aimed at the designing of pulse neutrongenerators (PNGs) with such time responses, is acomplicated problem that requires an effective solu�tion.

We will consider below two possible circuits forgenerating short neutron pulses. The first circuit cor�responds to quasi�stationary case, when the pulseduration of deuteron current considerably exceeds thedeuteron time of flight in the AT diode gap, and theaccelerating gap is almost always filled with a spacecharge of deuterons. In this case, the formation andacceleration of deuteron bunches in ATs can be

described to a high degree of accuracy using theBoguslavskii–Child–Langmuir (BCL) model. Accord�ing to this circuit, the short�pulse regime is imple�mented either due to a fast extraction of deuteronsfrom the plasma of the ion source by a strong electricfield or using a peaking spark gap.

The second circuit corresponds to the nonstation�ary case, when the pulse duration of deuteron currentis shorter than or on the order of the deuteron time offlight, and the accelerating gap is only partially filledwith a space charge. In this case, the BCL theory is notvalid, and the formation and acceleration of deuteronbunches should be simulated self�consistently usingthe Poisson equation together with the system ofdynamic equations, solving them by numerical meth�ods [6]. In this case, the regime of generation of shortneutron pulses must be implemented by using a specialsystem of formation of a short deuteron current pulseat the outlet of the ion source (see, for example [7]).

1. QUASI�STATIONARY MODEL OF GENERATION OF SHORT NEUTRON

PULSES IN PNGs BASED ON VNTs

In this case, the deuteron time of flight τtr in theaccelerating gap is determined from the equation

where e is the elementary electric charge, d is theaccelerating gap width, Md is the deuteron mass, andU(t) is the dependence of the accelerating voltage on

U t( ) td

0

t

∫ td

0

τtr

∫d

2Md

e��,=

Generation of Nanosecond Neutron Pulsesin Vacuum Accelerating Tubes

A. N. Didenkoa, A. E. Shikanova, V. I. Rashchikova, V. I. Ryzhkovb, and V. L. Shatokhina *a National Research Nuclear University Moscow Engineering Physics Institute (MEPhI), Moscow, 115409 Russia

b Dukhov All�Russia Research Institute of Automatics, Moscow, 127055 Russia*e�mail: [email protected]

Received June 20, 2013

Abstract—The generation of neutron pulses with a duration of 1–100 ns using small vacuum acceleratingtubes is considered. Two physical models of acceleration of short deuteron bunches in pulse neutron genera�tors are described. The dependences of an instantaneous neutron flux in accelerating tubes on the parametersof pulse neutron generators are obtained using computer simulation. The results of experimental investigationof short�pulse neutron generators based on the accelerating tube with a vacuum�arc deuteron source, con�nected in the circuit with a discharge peaker, and an accelerating tube with a laser deuteron source, connectedaccording to the Arkad’ev–Marx circuit, are given. In the experiments, the neutron yield per pulse reached107 for a pulse duration of 10–100 ns. The resultant experimental data are in satisfactory agreement with theresults of computer simulation.

DOI: 10.1134/S1063784214060061

ELECTROPHYSICS, ELECTRON AND ION BEAMS, PHYSICS OF ACCELERATORS

TECHNICAL PHYSICS Vol. 59 No. 6 2014

GENERATION OF NANOSECOND NEUTRON PULSES 905

time. The duration of the accelerating pulse may reachvalues of ~100 ns.

Two factors are responsible for the extraction of thedeuterons from the plasma of the ion source, namely,the thermal motion of deuterons and Langmuir oscil�lations in the region adjacent to the plasma boundary.During the process of extraction of deuterons from theplasma formation, its boundary shifts. The kinematicsof such movement is determined by the velocity fieldin the longitudinal shock wave formed upon theresponse of the deuteron source and by the decrease inthe longitudinal dimension of the plasma cloud due tothe removal of deuterons. The change in time of thelongitudinal coordinate of the plasma front can bedescribed by the following approximate differentialequation [8]:

(1)

with initial condition z(0) = h0. Here, z is the runninglongitudinal coordinate of the plasma front, h0 is thedistance from the point of the plasma formation to theaccelerating gap, b0 is the size of the plasma formationat the stage of hardening of its ionization state, n(t) isthe current concentration of deuterons and electronsin the plasma, Vd is the initial velocity of the plasmafront, j(z, t) = min{jBCL, jD},

is the BCL current density, f(u) is the compensationfactor of the space charge of deuterons by electronsfrom the cathode,

is the relative electron current, Ie and Id are the elec�tron and deuteron currents in the VNT acceleratinggap, m is the electron mass,

is the density of the deuteron emission current [8], RA

is the radius of the anode, θ0 is the initial temperatureof the plasma, and Nd is the number of deuterons in theplasma at the stage of hardening of its ionization state.

Analysis of Eq. (1) shows that at first the plasmaboundary moves in the direction of the cathode, andthen, as the concentration of deuterons decreases, itstops and begins to rapidly move back.

The time dependence of the accelerating voltagecan be obtained by solving the self�consistent systemof differential equations composed according to theKirchhoff rules for the equivalent electric circuit of the

dzdt��

Vd z h0+( )b0 Vdt+

�� j z t,( )en t( )��–=

jBCL z t u, ,( )4ε0

9�� e

Md

�� f u( )

h0 z d–+[ ]2��U t( )3/2≈

u m/Md Ie/Id( )=

jDeNd

πRA2 b0

�� 1Vdt

b0

��+⎝ ⎠⎛ ⎞

5/4–

≈

× 0.42eθ0

Md

��Vd

π��+⎝ ⎠

⎛ ⎞ 1 1Vdt

b0

��+⎝ ⎠⎛ ⎞

1/12–

+

PNG based on a pulsed high�voltage transformer incombination with Eq. (1).

To consider the processes of formation and accel�eration of deuteron bunches, we can use a simplifiedalgorithm by introducing the equivalent dynamic con�ductivity of the diode.

Calculating dependence U(t) for PNGs with apeaking spark gap characterized by breakdown voltageUb, we also used the same simplified system of equa�tions composed under the assumption of weak influ�ence of magnetization inductance on the formation ofthe accelerating voltage after the response of the peak�ing spark gap with initial condition U(0) = Ub. In thiscase, the time was measured from the instant of thespark gap response without taking into account tran�sient processes in it.

Instantaneous neutron flux in the VNT into a com�plete solid angle was calculated using the followingintegral expression [9]:

(2)

where

NA is the Avogadro number, A is the atomic number ofthe target carrier element, AH is the atomic number ofhydrogen isotope in the target (deuterium or tritium),AM is the atomic number of the target carrier metal(Ti, Sc, Zr), s is the stoichiometric coefficient in thetarget for heavy hydrogen, ρ(s) is the density of the tar�get material, ρM is the density of the carrier metal, Wis the kinetic energy of an accelerated deuteron (mea�sured in megaelectronvolts), χ(s) ≈ 1 + 0.02s is theswelling coefficient for the target upon its saturation,σ(W) is the microscopic cross section of a nuclearreaction, and F(W, s) are the deuteron energy lossesper unit length.

The dependences of the instantaneous neutron fluxΦ(t, u) for different values of relative electron currentu (reaction D(d, n)3He), calculated by formula (2),are shown in Fig. 1.

Analysis of these dependences shows a significantinfluence of emission electrons (parameter u) on thegeneration of neutrons for a limited energy stored inthe storage capacitor of the PNG high�voltage circuit.It boils down to a decrease in the amplitude and dura�tion of a neutron pulse upon an increase in parameteru that determines the number of emission electrons inthe VNT diode system.

Recalculation to reaction T(d, n)4He showed thepossibility of generation of neutrons per pulse at a levelof ≥108 for a pulse duration of ~100 ns.

Another conclusion that can be drawn on the basisof the computer experiment is the lower bound of theneutron pulse duration arising due to the finite time�

Φ t u,( ) G s( )Id t u,( ) σ W( )dWF W s,( )

��,

0

103–U t u,( )

∫=

G s( )NA

e�� sρ s( )

A AHs+��

NA

e��

sρM

AMχ s( )��,= =

906


DIDENKO et al.

of�flight of plasma in the cylindrical shielding elec�trode covering the deuteron source, estimated by theh0/Vd ratio; in the case of vacuum�arc deuteron source(VADS) [9], this ratio cannot be arbitrarily small dueto the finite size of the source. Therefore, the circuitfor generating nanosecond neutron pulses in a VNTbased on VADS without a peaking spark gap hasshown little promise. In this case, it is expedient to usea laser source of deuterons (LSDs) [9, 10].

Characteristic curves Φ(t, u) calculated for a PNGwith a peaking spark gap (Ub = 100 kV) for various val�ues of a relative electron current (reaction D(d,n)3He), obtained in the time range 1–30 ns withouttaking into account the transition process in the dis�charger, are shown in Fig. 2. The estimated time forwhich Φ(t, u) increases from 0 to a maximum valueis ~1 ns.

2. CHARACTERISTIC FEATURES OF GENERATION OF NEUTRON PULSES

WITH A DURATION LESS THAN OR COMMENSURATE WITH DEUTERON

TIME�OF�FLIGHT IN THE VNT ACCELERATING GAP

In this case, the deuteron time�of�flight in theaccelerating gap is determined by the following for�mula:

Here, τ is the duration of the accelerating pulse at thebase.

The corresponding calculations show that the deu�teron time�of�flight in small ATs can vary from 2 to

τtr τ U t( ) td

0

τ

∫⎝ ⎠⎜ ⎟⎛ ⎞

1–Mdd2

e�� U t( ) td

0

ω

∫ ωd

0

τ

∫–⎩ ⎭⎨ ⎬⎧ ⎫

.+=

10 ns. In this case, the formation and acceleration ofthe deuteron bunches cannot be generally described interms of the BCL quasi�stationary model since most ofthe time the diode accelerating gap is not completelyfilled by the space charge of deuterons.

To analyze the processes of acceleration of deuter�ons and generation of neutrons in this regime, we usednumerical simulation by approximately solving thePoisson equation self�consistently for potential ϕ ofthe electric field on a computer in cylindrical coordi�nate system (r, z), as well as the dynamic system ofequations

where ρ(r, z) is the self�consistent charge density inthe accelerating gap of the diode; qkα, μkα, rkα, and vkα

are the charge, mass, radius vector, and velocity of theenlarged particle with number kα, respectively. Indexk determines the composition of a large particle (k = 1and k = 2 correspond to electrons and deuterons,respectively), and α is the number of a large particle.

In the computational model used here, the realparticles are combined into larger particles, the num�ber of which is smaller than the number of real parti�cles by many orders of magnitude (particle�in�cellmethod). The field values that fill the entire space of

1r�� d

dr��rdϕ

dr�� d2ϕ

dr2��+

= ρ r z,( )ε0

��

dvkα

dt��

qkα

μkα

��∇ϕ rkα( ),–=

drkα

dt�� vkα,=

⎩⎪⎪⎨⎪⎪⎧

–

2.0 × 1013

1.5 × 1013

1.0 × 1013

5.0 × 1012

0 0.05 0.10 0.15 0.20t, μs

5

4

3

2

1

Fig. 1. Time dependences of instantaneous neutron fluxΦ(t, u): Φ(t, 0.5) (1), Φ(t, 0.1) (2), Φ(t, 0.05) (3),Φ(t, 0.01) (4), and Φ(t, 0) (5).

1 × 1014

5 × 1013

0 0.01 0.02 t, μs

4

3

2

1

Fig. 2. Time dependences of instantaneous neutron fluxΦ(t, u) (circuit with a peaking spark gap): Φ(t, 0.5) (1),Φ(t, 1) (2), Φ(t, 1.5) (3), and Φ(t, 2) (4).

Φ, neutrons/sΦ, neutrons/s



the physical system are approximately represented bythe values at regular mesh points.

The accepted model is collisionless in which thereis no interaction as such at the level of microparticles.In this case, the material points are smeared into con�tinuous formations and the differential operators arereplaced by finite�difference approximations on themesh. The potentials at the location of a large particleare calculated by interpolation over an array of meshvalues. The mesh densities are calculated by using theinverse�time procedure of distributing the particlecharacteristics to the next mesh points. Number N(t)of particles varies with time due to the arrival (emis�sion, injection) and departure of particles through theboundaries of the region.

As a result of the computer experiments, the fol�lowing pattern of filling of a diode by deuterons wasestablished.

At the first stage, the deuterons emitted from theanode gradually fill the entire diode space; but thenumber of deuterons at the anode increases continu�ously. This is due to the fact that as the diode is filled,the Coulomb eigenfield of the deuterons inside thediode increases with diode filling, and a strong longi�tudinal field decelerating the deuterons appears at theanode. After completion of the pulse supplied to thediode, the emission stops, and the remaining deuter�ons leave the diode space. The Coulomb field of thebeam in the diode gradually decreases at this stage. Asthe beam moves towards the cathode, its uniformity isviolated and its radius increases, which can beexplained by the influence of the Coulomb eigenfield.In this case, some deuterons do not reach the cathode.The eigenfield of the deuteron flow turns out to becomparable in the order of magnitude with the exter�nal field, which causes its spreading in the longitudinaland transverse directions.

We also calculated the dependencies of flux Q ofaccelerated deuterons falling on the AT target on theemission current from the deuteron source and width

d of the accelerating gap for a fixed amplitude of thevoltage across the accelerating gap (Fig. 3). It can beseen from Fig. 3 that the curves have a smooth peak.The slope of the right part of the curve is connectedwith the diode cutoff by the space charge and spread�ing of the deuteron current.

The differential energy spectra dq/dW of deuteronsat the outlet, calculated for two values of deuteroninjection current Iin, are shown in Fig. 4. The charge ofdeuterons is plotted along the vertical axis and theenergy is plotted along the horizontal axis. It can beseen from Fig. 4 that the deuteron spectrum spreadswith an increase in the injection current, which is alsodue to the influence of the space charge. Smearing ofthe spectrum is caused by the presence of the beameigenfield.

The resulting energy spectra have made it possibleto calculate the neutron yield per pulse from the fol�lowing formula:

(3)

where nn is the concentration of the target carriermetal and

is the charge of a group of deuterons corresponding toenergy Wi (MeV). The calculation was performed for a

Φsnn

eτ�� qi

σ W( )F W( )�� W,d

0

W

∫i

∑=

qidqdW��

Wi

Wi Wi 1––( )≈

1.1 × 1012

7.4 × 1011

3.9 × 1011

4.7 × 1010

0 5 10 15 I, A

Ψ, D/s

3

2

1

Fig. 3. Characteristic dependences of the deuteron flux onthe emission current for different widths of the diode gap:0.01 (1), 0.0075 (2), and 0.005 m (3).

(a)

(b)

1.2 × 10−9

7.8 × 10−10

3.9 × 10−10

0

1.9 × 10−9

1.3 × 10−9

6.4 × 10−10

020 40 80 120

E, keV

Q, C

Q, C

Fig. 4. Energy spectra of accelerated deuterons at the tar�get for different deuteron emission currents Iin: 1 (a) and15 A (b).

908


DIDENKO et al.

titanium target (s = 1) at a voltage of 100 kV and apulse duration of 10 ns.

The calculated characteristic dependences of theinstantaneous neutron flux emitted by a VNT on thedeuteron emission current and on the duration of ahigh�voltage pulse for a constant deuterons injectioncurrent are shown in Fig. 5.

The calculated dependences of the instantaneousneutron flux emitted by a VNT on the deuteron emis�sion current and on the duration of the deuteron injec�tion current pulse at a constant voltage (100 kV) acrossthe accelerating gap are shown in Fig. 6. In our calcu�lations, the shape of the injection current pulse wasassumed to be rectangular. For this case, we also usedformula (3), in which parameter τ was replaced by theduration of the deuteron injection current pulse.

The calculation showed that the value of the peaktotal instantaneous neutron flux can reach a value of~1014 neutrons per second in reaction T(d, n)4He.Like in Fig. 2, these curves demonstrate the manifes�tation of cutoff effect for various durations of theaccelerating voltage pulse. Starting from a current 10 Aand durations exceeding 20 ns, the cutoff of the diodeby a space charge takes place. At higher currents, thecutoff occurs earlier.

The dependences of the neutron flux on the accel�erating voltage were investigated separately. Weobserved a monotonic increase in the neutron fluxwith voltage and virtually no influence of the emissionelectrons on the generation of neutrons.

3. EXPERIMENTAL INVESTIGATIONOF WORKING PROTOTYPES

OF GENERATORS OF SHORT NEUTRON PULSES

We studied experimentally two circuits for neutrongeneration. In the first circuit (Fig. 7), a high�voltagepulse transformer (PT) was used in combination witha peaking spark gap connected in series with a vacuumAT based on a VADS.

The general view of the emitter is shown in Fig. 8.It consists of a high�voltage PT, an accelerating voltagepulse former, a VNT, and a trigger circuit of the ionsource. All these units were located in the cylindricalcasing with dimensions of ∅110 × 500 mm. Trans�former oil served as an insulator. The coaxial locationof the elements and the absence of connecting con�ductors (all the contacts were effected by the workingsurfaces) ensured minimal values of parasitics.

The values of capacitances C2 and C3 (see Fig. 7) inthe circuit of peaking spark gap K2 were chosen within50–100 pF, inductance L2 was within 0.5–2 μH, andresistance R2, within 300–2000 Ω. As the peaker, weused a high�pressure discharger with a pickup voltageof 40–60 kV, switching time tk = 3 ns, switching energy0.5 J, and operating frequency 100 Hz.

3.5 × 1012

2.4 × 1012

1.2 × 1012

5.5 × 10105 10 15 20 25 t, ns

Φ, n/s

65 4

3

Fig. 5. Dependences of the instantaneous neutron flux (inrelative units) on the pulse duration of the acceleratingvoltage; Iin: 0.5 (1), 1 (2), 5 (3), 10 (4), 15 (5), and 20 A (6).

3

2

1

4

5 9 12 16 19 23 26 t, ns

Φ, a. u.

12

6

5

4

3

Fig. 6. Dependences of the instantaneous neutron flux (inrelative units) on the pulse duration of the deuteron injec�tion current; Iin: 0.5 (1), 1 (2), 5 (3), 10 (4), 15 (5), and20 A (6).

U0

K1

T1

C1

C2R2

K2L1

R1 C3

M AI

C4 C5

L2

L3 T2

K

Fig. 7. Basic electric circuit of the experimental emitter ofneutron pulses in the nanosecond range.

Fig. 8. General view of a working prototype of a small gen�erator of short neutron pulses.

2

1



Short neutron pulses are formed in the followingway. Capacitors C1 and C4 are charged by direct voltageU0. When a control pulse is supplied to the trigger elec�trode of commutator K1, the latter responses, andcapacitor C1 is discharged to primary winding T1 of thehigh�voltage PT. A high�voltage pulse formed on itssecondary winding is supplied to the circuit forming ananosecond voltage pulse including peaking sparkgap K2. The resultant high�voltage pulse is supplied tothe accelerating gap. Simultaneously, a trigger pulse,which actuates the ion source, is formed in the VADScircuit (L2, L3, C5, and T2) on electrode I. In this case,capacitor C4 is discharged through the anode (A)–cathode (K) path of the VNT VADS. The deuteronsaccelerated by a short high�voltage pulse to target (M)are formed in the arc discharge plasma. Neutrons weregenerated on a tritium target according to nuclearreaction T(d, n)4He. Experimental oscillograms areshown in Fig. 9.

Neutron measurements were taken by the methodof recoil protons formed in the scintillator, as well as bythe activation method. The neutron pulse durationwas about 40 ns at half�amplitude. The neutron yieldwas ~ 1 × 106 per pulse at charging voltage U0 = 5 kVand capacitance C1 = 0.1 μF of the reservoir capacitor.The resultant data agree with the computer simulationdata.

The second circuit for generating short neutronpulses is based on the possibility of fast extraction of alldeuterons from the laser plasma by supplying a voltagepulse with a large amplitude (>300 kV) to the acceler�ating gap of the VNT from the LSDs. It was imple�mented in a neutron emitter combining AT with LSDsand pulse voltage generator (PVG) according to the

Arkad’ev–Marx generator scheme, which makes itpossible to obtain high�voltage pulses of up to 500 kV.The diagram of experimental setup is shown in Fig. 10(1—high�voltage PVG, 2—cell with an insulating liq�uid, 3—VNT, 4—lens, 5—beam splitter, 6—coaxialphotocell, 7, 8—neutron recording system, 9—pulsed laser, 10—laser PVG, 11—laser control unit,12—oscilloscope, 13—Rogowski loop, 14—con�trolled delay line, 15—charger, and 16—unit trigger�ing the pulse voltage generator).

In the experiment, we used a VNT with an LSD inwhich the plasma was formed under the action offocused radiation of a pulsed yttrium–aluminum gar�net laser. An accelerating pulse on the diode gap of theAT was formed by using a compact two–stageArkad’ev–Marx PVG located in a metal pressure�resistant shell the interior of which was filled with SF6gas under a high pressure. Such a PVG has made itpossible to form the accelerating pulse with an ampli�tude of ≈300 kV and a duration of ~100 ns at a half�amplitude. The radial dimension of the PVG did notexceed 0.15 m. The energy stored in the PVG capaci�tors was about 1 J.

The diagram under consideration differs from theprevious one in that it does not use a peaking spark gapand the neutron pulse is shortened by a fast extractionof deuterons (advancing heavy ions) from the plasmadue to a high value of the BCL current, ensured by ahigh value of the accelerating pulse amplitude.

Neutrons were generated on a tritium targetaccording to nuclear reaction T(d, n)4He.

During neutron measurements, we used a scintilla�tion detector that implements the recoil protonmethod. These neutron measurements were simulta�neously monitored by an “all�wave” detector [1],which increased the reliability of determining the neu�tron yield.

In this experiment, the average neutron yield perpulse reached a value of ≈2 × 107 with the pulse dura�

UC2

UI

I

U

n

200 400 600 800 t, ns

Fig. 9. Oscillograms of the voltage pulses on capacitor UC2,trigger electrode UI, current I through the VADS, acceler�ating voltage U, and neutron pulse n.

16

15

14

2

4 59

10

1112

13

R3

3

6

7 8

R1

Fig. 10. Diagram of the experimental setup for testing thePNG prototype based on a VNT with an LSD andArkad’ev–Marx PVG.

1

R2

910


DIDENKO et al.

tion of about 100 ns at half�amplitude. In this case, theamplitude of the accelerating pulse did not exceed300 kV, and its duration at half�amplitude heightranged from 150 to 180 ns.

In this case, the total energy accumulated in thecapacitive storages of Arkad’ev–Marx PVGs and ofthe laser was approximately 50 J. Thus, the value of aneutron generated in the experimental setup was at alevel of ≈2.5 × 10–6 J/neutrons, which approximately isan order of magnitude higher than the value of a neu�tron obtained from neutron emitters with an LSD inmicrosecond range [10].

The resultant experimental data lead to the conclu�sion that by increasing the amplitude of the accelerat�ing pulse, lockstep synchronization of laser actuationwith PVG triggering, enhancing the stability of the lat�ter in the frequency mode, and increasing the effi�ciency of the laser, it is possible to construct the oper�ating device with an average neutron flux into a com�plete solid angle of ~109 neutrons/s and a pulseduration of not more than 100 ns at a half�ampli�tude. In this case, the value of the neutron can reach~10–7 J/neutrons.

In the experiments on generation of short neutronpulses described above, as well as in computer simula�tion, it is necessary to suppress more effectively theelectrons emitted by a neutron generating target toincrease the accelerating voltage and the ion current.Here, it is quite promising to use the idea of magneticinsulation of the accelerating gap of the tube by thespiral line field [11]. The experiments with such diodesystems on a dismountable prototype of the VNT haveshown that generation of up to 108 neutrons per pulseon reaction D(d, n)3He is possible.

CONCLUSIONS

1. In generating short neutron pulses in a VNT, tworegimes of formation and acceleration of deuteronbunches should be distinguished, i.e., when the timelength of the bunch considerably exceeds the time�of�flight of a deuteron in the accelerating gap and when itis shorter then or commensurate with the time�of�flight. In the latter case, it can be assumed that theaccelerating gap is only partially filled with a spacecharge.

2. For the first regime, the computer simulation hasshown that the neutron yield and the duration of theneutron pulse are significantly reduced with increasingelectron emission current from the cathode of theVNT diode system.

3. For the second regime, it was found as a result ofcomputer simulation that the Coulomb deuteroneigenfield is commensurate with the external acceler�ating field and significantly affects the formation andacceleration of deuteron bunches by decelerating deu�terons in the anode region, the spreading of the deu�

teron flow in the transverse direction, and its energyspectrum.

4. The experimental results on generation of shortneutron pulses in a VNT concerning the measure�ments of the neutron yield agree in the order of mag�nitude with the results of computer simulation.

5. The energy value of neutrons generated in thesetups being considered may exceed by an order ofmagnitude or more the value of neutrons generated inVNTs in the microsecond range of neutron lifetime.

6. The lower bound of the duration of a neutronpulse appears due to the finite time�of�flight of theplasma from the region of its formation to the acceler�ating gap.

7. The resultant measurements of the neutron yieldin the experimental PNGs indicate that even at thelevel being considered, the investigated circuits forneutron generation satisfy in principle the require�ments to the neutron flux and pulse durations,imposed by the remote control techniques mentionedin the Introduction.

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Translated by N.V. Wadhwa

generation of nanosecond neutron pulses in vacuum accelerating tubes

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