- Email: [email protected]
The study of neutron burst shape of a neutron tube driven by dispenser cathode
Nuclear Instruments and Methods in Physics Research A 828 (2016) 91–96
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
The study of neutron burst shape of a neutron tube driven by dispenser cathode Evgeny Grishnyaev n, Sergey Polosatkin Budker Institute of Nuclear Physics, Russia
art ic l e i nf o
a b s t r a c t
Article history: Received 25 January 2016 Received in revised form 11 April 2016 Accepted 6 May 2016 Available online 11 May 2016
A slim-shaped portable DD-neutron generator is developed at Budker institute of Nuclear Physics. The generator is a combination of Cockcroft–Walton voltage multiplier and a sealed gas-filled neutron tube driven by dispenser cathode. Neutron burst shape in pulsed mode of neutron tube operation is measured with stroboscopic time spectrometry, implemented on scintillation detector, and modeled with Comsol Script 1.3 and Comsol Multiphysics 3.5. Modeling appears to be in good agreement with experimental results. Measured pulse rise and fall times are 110 ns and 100 ns respectively. & 2016 Elsevier B.V. All rights reserved.
Keywords: Neutron generators Ion sources Finite element modeling
1. Introduction A slim-shaped pulsed DD-neutron generator for science and industry is developed at Budker Institute of Nuclear Physics (BINP). The generator comprises Cockcroft–Walton voltage multiplier and gas-filled neutron tube. Penning-type ion sources are commonly used in neutron tubes for logging tools [1–5]. The basic distinction of neutron tube developed at BINP from the most of commercial gas-filled neutron tubes is utilization of a dispenser cathode ([6], barium dispenser cathode is heated indirectly by a filament, see Fig. 1) in ion source. This development is made in pursuit of short fronts of neutron bursts. One of the values, that characterize pulsed mode of operation of neutron generator, is a pulse rise and fall time, defined as time interval between the moments when neutron yield reaches 90% and 10% of maximum value. Particularly the pulse fall time is of great importance in pulsed neutron well logging technology (particularly, in inelastic gamma ray spectroscopy) [3]. Modern gas-filled neutron tubes with conventional Penning-type ion sources produce neutron bursts with rise time of 2 μs and fall time of about 1 μs [3,7]. The shape of neutron bursts is reported to be different among neutron generators of one type [8]. “Thermo scientific” company reports the best result – neutron generator P 385 with rise/fall time of 1.5/0.5 μs [9,10]. One of possible approaches to minimize the rise/fall time is utilization of dispenser cathode in ion source of neutron tube. This kind of neutron tube (called “Minitron”) was pioneered at n
Correspondence to: Lavrientev avenue, 11, Novosibirsk, Russia. E-mail address: [email protected] (E. Grishnyaev).
http://dx.doi.org/10.1016/j.nima.2016.05.021 0168-9002/& 2016 Elsevier B.V. All rights reserved.
Schlumberger company in 1991 [11] and successfully applied for pulsed neutron logging until now. “Minitron” is the first and the only commercial neutron tube with ion source driven by dispenser cathode. Schlumberger never discloses the details of engineering calculations involved in the process of equipment development, so, this work together with [12] are the first ones elucidating the approach to calculation-based development of compact neutron tube with ion source driven by dispenser cathode. Typically, the logging tools utilize DT-neutron generators. This paper presents the modeling results and benchmarking of the model performed on the DD neutron generator. The neutron burst shape evaluation using the DD neutron generator is driven by the safety considerations, while the main conclusions are applicable for DT generator.
2. General description of neutron tube A neutron tube consists of the ion source, gas source, accelerator column and a target. The target is made of the material that is saturated with deuterium prior to use of the neutron generator. The nuclear reaction takes place on the titanium target, when the accelerated deuterium ions collide with the deuterium atoms implanted in the titanium layer [13], resulting in the 2.45 MeV neutrons: Dþ D-3He(0.82 MeV) þn(2.45 MeV). Commercial sealed DD-neutron tubes produce 106 n/s with 50 μA of ion current and 80 kV of accelerating voltage [14]. The simplest case of a neutron tube for computer modeling is axially symmetric tube with ion source driven by dispenser cathode without magnetic field (Fig. 1). The principle of operation of this kind of tube is the following. Grounded cathode is placed close
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E. Grishnyaev, S. Polosatkin / Nuclear Instruments and Methods in Physics Research A 828 (2016) 91–96
of getter heating current). Standard mode of neutron generator operation is 0.5 Pa of deuterium pressure, 10 mA electron emission current, pulsed 200 V anode voltage, 100 V extractor voltage, 50 μA ion current and 81 kV accelerating voltage.
3. The concept of plasmaless neutron tube As reported earlier [12], the tube can be thoroughly modeled with any modeling software based on finite element method (FEM) with particle tracing subroutine, provided electric field in ion source is high enough and space charge buildup does not lead to formation of potential extremums. Generally speaking, any modeling of deuterium-filled neutron tube should consider somehow all elementary processes (Table 1). Each process can affect distributions of electron and ion space charge densities in ion source and ion current density profile on target. Modeling, described in detail in [12] and in this paper, neglects influence of processes 1–3 on electron charge density distribution and processes 4–6 on ion charge density distribution. Validity of such simplification should be verified after completion of modeling. Estimation of probabilities for all neglected processes at nominal operating conditions gives the following results:
Fig. 1. Schematic representation of the neutron tube.
to the anode with a potential of about 200 V. The cathode uniformly emits electrons from its surface. Electrons accelerated with anode field traverse the inner volume of hollow anode until disappearing on electrodes (anode or extractor). Energetic electrons introduce ionization in the volume of ion source. Ions are extracted and directed to the target. Electrostatic field in two-electrodes ion optics, comprising the extractor and suppressor of secondary electrons, accelerates ions. The extractor is held under some constant voltage about 100 V to prevent ions from reaching the target after anode potential has switched to zero. The suppressor is connected directly to high voltage power supply. The target is connected to the suppressor through 8 MOhm resistor to make its potential less negative than suppressor potential during ion current flowing through the target. It prevents secondary electrons from leaving the vicinity of the target. The source of deuterium in the tube is a getter strip (we used St101 getter produced by SAES Getters [15]). Getter irreversibly adsorbs all gases except hydrogen isotopes, which are adsorbed reversibly. Equilibrium deuterium pressure in sealed volume of the tube depends on getter temperature, which is controlled with heating current. The higher the heating current, the higher the deuterium pressure. Ion beam current can be controlled in 2 ways: (1) changing of cathode emission current (through adjustment of cathode heating current), (2) changing of deuterium pressure (through adjustment
1. Total probability for electron to take part in the processes 1 or 2 or to undergo 1 “effective” elastic collision with D2 molecule is P123 ¼0.025 2. Ions in ion source are accelerated by more than 20 eV/mm. Under these conditions probability of D3 þ ion formation from D2 þ is below P4 ¼0.02. 3. Total probability for deuterium ion to undergo charge exchange or “effective” elastic (polarization) collision with D2 molecule in IS ion source is below P56 = 0.1 4. Mean total probability for deuterium ion to undergo charge exchange or “effective” elastic (polarization) collision with D2 tot molecule on its whole trajectory is P56 = 0.24 IS For self-consistent potential field estimation P56 is much more tot important than P56 , because potential field and space charge field are almost absolutely decoupled in ion optics (region of vacuum tot electrostatic field intensity about 27 kV/cm), but rather high P56 nevertheless means that exact replication of modeled ion current density on neutron generating target in real experiment cannot be expected. The degree of discrepancy between the modeled and experimentaly obtained current density profiles is still an object of experimental study. All probabilities, characterizing elementary processes in ion source, are shown to be low and self-consistent field can be simply modeled on the basis of freely moving particles tracing [12]. Our model includes only reactions of ionization (№1 in the Table 1). The absence of the irregularities in the electrical potential field in the ion source suggests that this ion source and entire tube can be referred to as plasmaless.
Table 1 Elementary processes taking place in DD-neutron tube. №. Elementary process 1 2 3 4 5 6
Dissociative ionization: D2 þ e-D þ þ Dþ 2e Nondissociative ionization: D2 þ e-D2 þ þ2e Inelastic scattering of electron on D2-molecules Elastic scattering of electrons on D2-molecules D2 þ þ D2-D3 þ þD Elastic scattering of ions on background D2 gas Charge exchange between ions and background D2 gas
Cross-section the sum of cross-sections for 200 eV electrons is 9 10 17 cm2 [16] total cross-section of D2-molecule excitation for 200 eV electrons is 2.9 10 16 cm2 [16] elastic scattering momentum transfer cross section for 200 eV electrons is 1.7 10 17 cm2 [17] cross-section reaches 10 14 cm2 at thermal ion energies and rapidly decreases at energies above 1 eV [18] described with momentum transfer cross-section of polarization interaction [19, 20] Cross-section data can be found in [19, 20]
E. Grishnyaev, S. Polosatkin / Nuclear Instruments and Methods in Physics Research A 828 (2016) 91–96
Plasmaless tube can be thoroughly modeled with stationary iterative method, described in [12]. In pulsed plasmaless mode (when voltage on anode is represented with square wave) transient process of ion current appearance and disappearance also can be thoroughly modeled.
4. Modeling of ion flow appearance The potential difference between the extractor and the anode is always 100 V (the sign of potential difference depends on current phase of anode square wave). So, the electric field is always strong enough to be considered as close to vacuum field (Fig. 2) and effects of space charge in the modeling of ion flow appearance are neglected. Another simplification follows from that electrons move more than 86 times faster than D2 þ ions (rough estimation of velocities ratio in the same electric field is mi = 4⋅1840 ≈ 86, me
but the fact that electrons are accelerated in the strongest field in “cathode–anode” region makes this ratio an estimation from below). Further treatment supposes that electron flow appears and disappears instantly. The approach to ion flow modeling is the same as in [12]: complete ion flow on the target consists of a set of current-bearing ion trajectories that start at the nodes of FEMmesh with nonzero ion birth rates. For every trajectory the timeof-flight is known from the particle tracing subroutine. The transient process is modeled in Comsol Multiphysics 3.5 and Comsol Script 1.3. The result of modeling is a sequence of time moments and according sequence of ion current values representing transient process. Consider the moment of time when rising front of square wave appears on the anode. This moment is represented by 2 values: time ¼0, current¼ 0. Each next column contains time-of-flight for trajectory and total ion current as cumulative sum of elementary ion currents. Columns are sorted by time in increasing order. Time profile of ion current appearance is shown on Fig. 4. One can see, that rather strong extracting field together with small size of ion source allows all ions to reach target in less than 150 ns for 90% of ions.
5. Modeling of ion flow disappearance When anode potential sharply switches from 200 V to zero electrons also disappear instantly as compared to ions. All ions, following those trajectories that end on target, can be divided onto 2 groups: (1) ions that have enough kinetic energy to overcome braking field and to be extracted to target, (2) ions that have not
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been accelerated enough to overcome braking field and disappear in ion source. Now every ion trajectory, modeled for 200 V at anode, is considered not as a stationary current-bearing streamline, but as a set of ions with different initial energies. These ions are aligned along the trajectory at initial time moment and reside at the points of trajectory discretization. The first task now is to figure out what ions can overcome braking field and what ions cannot. The second task is to estimate momentary values of currents carried by ions reaching the target. The correspondence of ions times-of-flight to momentary currents forms the waveform of particular streamline decay after anode voltage switches to 0. Every ion trajectory, modeled for the case of 200 V at anode, is analyzed this way. The example of this analysis is shown on Fig. 3. Modeling script starts from the first ion (that has zero kinetic energy) and checks if this ion reaches the target (see the set of solid trajectories ending inside the ion source in Fig. 3). If it does, the particle tracing subroutine estimates time-of-flight for this ion (see the last solid trajectory in Fig. 3. This trajectory leaves ion source and ends on target surface) and the script moves to the next ion along the trajectory and so on to the last point of a streamline. The result of streamline analyzing is a correspondence of a set of ions times-of-flight TOFt i (i is an index enumerating vertexes of a streamline corresponding to ions reaching the target) in “Off” field and a set of particle time values at streamline vertexes partTt i (this is the time counted from the origin of a streamline) in “On” field. One can estimate a waveform of a streamline current decay (set of decay
I i values at times
TOF
t i ) as
decay
Ii =
str
partT
I
t i + 1 − partTt i
TOF
t i + 1 −TOFt i
, where
str
I is a
stationary streamline current in “On” field. Examples of modeled waveforms are presented on Fig. 3. Every waveform has nearly flat part in the beginning. It corresponds to ions that traverse accelerating gap when anode voltage switches to 0 V. Decaying part corresponds to ions residing in ion source at the moment of switching. The time profile of total ion current decay is the sum of elementary current decay waveforms estimated for all streamlines (Fig. 4, right). One can see, that rather strong braking field together with small size of ion source allows only fast ions to reach target after anode voltage switches to 0 V. And it takes less than 150 ns for 90% of fast ions.
6. Measurement of neutron burst shape There are two possible approaches to study neutron burst
Fig. 2. Potential field in ion source of neutron tube with 200 V on anode (“On” field, left) and with 0 V on anode (“Off” field, right). Equipotential lines are shown in increments of 10 V.
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Fig. 3. Left: Example of D2 þ -ion trajectory analyzing. Thick dashed line is current bearing streamline modeled for 200 V at anode. Solid lines are ion trajectories modeled for 0 V at anode. For convenience of visual perception only the 1st trajectory reaching the target is shown. Right: 3 examples of modeled waveforms of elementary currents decay.
shape. The first (and the most obvious) one is to measure it directly with the method of time spectrometry (see, for example, [21]). The second way is to measure the waveform of ion current on target, bearing in mind that momentary value of ion current is proportional to momentary neutron yield. Ion current oscillography can explicitly approve or disprove repeatability of single pulses shape. And this is the apparent advantage of ion current oscillography over neutron output time spectrometry. But this advantage is valid only if one makes an extra effort to monitor the dynamics of secondary emission, beam spot size during ion source switching, stability of accelerating voltage during switching events and several other effects. Under these circumstances direct measurement of neutron pulse shape is significantly simpler and cheaper than ion current oscillography. To say nothing of the fact that only neutron time spectrometry can be considered as absolute proof that rise/fall time is equal to one value or another. Another argument in favor of time spectrometry is that pulse-to-pulse stability is not important in neutron technologies, because spectra of secondary particles (for example, scattered neutrons or characteristic γ-quanta in well-logging) are accumulated over many pulses and only integral neutron pulse shape really matters. So, time spectrometry is chosen to measure neutron burst shape. Scintillation neutron detector, developed earlier at BINP, is selected as major detector for fast neutron measurements [22]. Terphenyl crystal with dimensions ∅40 40 mm is used as a scintillator, photomultiplier (PMT) Hamamatsu R6231-100 is applied for scintillation flashes detection. Registration unit is
developed by BINP electronics group for PMT pulses analysis. The unit includes fast ADC and programmable logic array for preliminary pulses processing. ADC parameters are the following: counting rate 500 MHz, dynamic range 12 bit, memory 3 106 counts. These parameters are sufficient for direct measurement of stilbene scintillation pulse shape. It opens additional possibilities for neutron radiation analysis. Built-in programmable logic arrays algorithms are capable of real-time signal preprocessing and implementation of different modes of operation of the unit. Currently, the following operation modes of the unit are implemented: (1) oscilloscope mode for registration of input signals waveforms, (2) pulse shape registration mode (n-γ-discrimination) – for each scintillation pulse the 1 μs waveform portion is recorded, (3) count mode – the number of events for a given time interval is counted, (4) stroboscope mode with n-γ-discrimination – for each event a delay from reference pulse synchronized with anode pulse is stored in statistics. The last mode allows to measure temporal characteristics of a neutron flux.
7. Results and discussion The results obtained in the experiment on stroboscopic time spectrometry of pulsed neutron output together with fronts shapes predicted with modeling are shown at Fig. 4. One can
Fig. 4. Comparison of modeled waveforms of ion current appearance (left) and disappearance (right) with experiment. Solid lines are modeled waveforms. O-symbols represent time spectra of neutron bursts. Deviation bars are estimated as mean square deviation in Poisson's distribution (as square root of neutron yield).
E. Grishnyaev, S. Polosatkin / Nuclear Instruments and Methods in Physics Research A 828 (2016) 91–96
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Fig. 5. Left: Modeled current decay waveforms for 2 extractor grids with different geometrical transparency: thick gray curve – L ¼ 0.65 mm, thin black curve – L ¼ 0.5 mm. Right: graphical explanation of how L is defined.
observe good agreement between modeling and experiment for the front edge of neutron burst, but there is some discernible difference between measured rear front and modeled one. Possible cause of this circumstance is the fact that ion current fall time depends on geometrical transparency of extractor grid (Fig. 5) while there is no such dependence for rise time. Indeed, “On” field accelerates ions and makes them traverse extractor grid rapidly [12]. Thus, rise time depends only on “macroscopic” geometrical characteristics of extractor grid (i.e., cone angle only) that define “far” field in the ion source (i.e. on the distances greater than L from the cone surface). “Off” field decelerates ions. It means that last streamline ions reaching the target (they correspond to decaying parts of elementary current waveforms, Fig. 3) spend a lot of time near the extractor grid (because of low initial energy) and their trajectories are strongly affected by detailed stricture of electrostatic field near the grid (“near” field), that is defined by “microscopic” geometrical characteristics of the grid (i.e. the value of L). See how last solid trajectory on Fig. 3 is distorted near the extractor grid. Thus, fall time depends not only on cone angle, but also on L. Real extractor grid, placed in the neutron tube, is made of square-celled grid with square side 0.5 mm and its shape is not ideally conical. Time delay between neutron yield reaching 10% and 90% of maximum (formal rule defining rise and fall time) is 110 ns for rise time and 100 ns for fall time.
8. Conclusion Neutron tube with ion source driven by dispenser cathode is developed at Budker Institute of Nuclear Physics. The tube is referred to as “plasmaless” tube, because extracting electric field in ion source is made high enough to extract ions rapidly, so space charge effects are of no significance in tube operation. Rise and fall times of neutron bursts, predicted with modeling in the frameworks of “plasmaless” approach, are in good agreement with experimental results of stroboscopic time spectrometry of pulsed neutron output. Measured rise and fall times are 110 ns and 100 ns accordingly. Neutron generator utilizing this tube is currently being exploited at BINP for calibration of cryogenic avalanche detector of weakly interacting particles. Another verification of plasmaless neutron tube operation theory is comparison of target erosion profile with modeled current density distribution. Of course, it can
be performed only after neutron tube malfunction.
Acknowledgments The development of modeling means was supported by Russian Science Foundation under grant N 14-50-00080. Manufacturing and activation of neutron tube and experimental measurement of neutron burst shape was supported by Russian Foundation for Basic Research under project No. 16-32-00042 mol_a.
References [1] L.A. Shope, et al., Operation and life of the zetatron: a small neutron generator for borehole logging, IEEE Trans. Nucl. Sci. 28 (2) (1981) 1696–1699. [2] E. Bogolyubov, I. Titov, T. Khasaev, et al., The development and production of neutron tubes, neutron generators and equipment for pulsed neutron logging, in: Proceedings of Novel Technologies in Geophysics Sypmposium, Ufa, Russia, 22–24 May 2001, pp.126–127. (in Russian). [3] M. Agalakova, S. Butolin, V. Chermensky, et al., Pulsed neutron generators designed by “Energiya NPP LLC” in well logging, Sci. Tech. Bull. “Karotazhnik” 222 (2012) 80–91 (in Russian). [4] V.G. Markov, D.E. Prokhorovich, A.G. Sadilkin, et al., Determination of the corpuscular emission energy characteristics for the ion sources of gas-filled neutron tubes, Adv. Appl. Phys. 1 (1) (2013) 23–29 (in Russian). [5] W. Lio, M. Li, K. Gao, et al., Discharge characteristics of a penning ion source for compact neutron generator, Nucl. Instrum. Methods Phys. Res. A 768 (2014) 120–123. [6] http://toriy.ru/en/kkpy.html (last accessed 04.04.16). [7] http://en.power-np.ru/pulsed-neutron-generators (last accessed 26.12.15). [8] V. Chermensky, Method and apparatus for pulsed neutron-gamma spectrometry logging for determination of operational oil saturation of exploited formations Doctoral thesis, Dubna, 2008, p. 64 (in Russian) [Online]. Available: http://power-np.ru/d/233622/d/dissertation.pdf (last accessed 26.12.15). [9] D.L. Chichester, J.D. Simpson, M. Lemchak, Advanced compact accelerator neutron generator technology for active neutron interrogation field work, J. Radioanal. Nucl. Chem. 271 (3) (2007) 629–637. [10] http://www.thermoscientific.com/en/product/p-385-neutron-generator.html (last accessed 26.12.15). [11] Neutron generator by F.K. Chen, A.D. Liberman, (1991, Nov. 27). US Patent 5 293 410 [Online]. Available: http://www.google.com/patents/US5293410 (last accessed 26.12.15). [12] E.S. Grishnyaev, S.V. Polosatkin, Modeling of deuterium ionization and extraction from an ion source driven by heated cathode, IEEE Trans. Plasma Sci. 43 (11) (2015) 3856–3867. [13] P.D. Lomer, D.S. Stark, J.D.L.H. Wood, Sealed-off neutron tubes, Nucl. Instrum. Methods 92 (4) (1971) 569. [14] E.S. Grishnyaev, S.V. Polosatkin, Yield determination for a titanium neutronforming target, At. Energy 113 (5) (2013) 345–350. [15] https://www.saesgetters.com/sites/default/files/St%20101%20Brochure_0.pdf (last accessed 04.04.16). [16] R.K. Janev, J.J. Smith, Cross sections for collision processes of hydrogen atoms with electrons, protons and multiply charged ions [Online], At. Plasma-Mater.
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Interact. Data Fusion (Suppl. J. Nucl. Fusion) 4 (1993), Available: 〈https://wwwamdis.iaea.org/ALADDIN/collision.html〉. [17] I. Bray, A.T. Stelbovics, Calculation of electrons scattering on hydrogenic targets, Adv. At. Mol. Opt. Phys. 35 (1995) 209–254 [Online]. Available 〈https:// www-amdis.iaea.org/ALADDIN/collision.html〉. [18] C.F. Barnett, Atomic Data for Fusion, Volume 1: Collisions of H, H2, He and Li atoms and ions with atoms and molecules, – Oak Ridge National Laboratory Report, 6086 1990, 145–147. [19] Yu Raizer, Physics of gas discharge, Dolgoprudny: Intellect, 2009, pp. 63–70. (in Russian).
[20] R.K. Janev, W.D. Langer, K. Evans, D.E. Post Jr., Elementary Processes in Hydrogen-Helium Plasmas, Springer Series on Atoms and Plasmas, SpringerVerlag, Berlin, Heidelberg, New York, 1987 [Online]. Available 〈https://wwwamdis.iaea.org/ALADDIN/collision.html〉. [21] F.K. Chen, Investigation of the striking characteristics of a Penning ion source, J. Appl. Phys. 56 (11) (1984) 3191–3197. [22] Yu.S. Sulyaev, E.A. Puryga, A.D. Khilchenko, et al., Multi-purpose fast neutron spectrum analyzer with real-time signal processing, Nucl. Instrum. Methods Phys. Res. Sec. A 720 (21) (2013) 23–25.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
The study of neutron burst shape of a neutron tube driven by dispenser cathode Evgeny Grishnyaev n, Sergey Polosatkin Budker Institute of Nuclear Physics, Russia
art ic l e i nf o
a b s t r a c t
Article history: Received 25 January 2016 Received in revised form 11 April 2016 Accepted 6 May 2016 Available online 11 May 2016
A slim-shaped portable DD-neutron generator is developed at Budker institute of Nuclear Physics. The generator is a combination of Cockcroft–Walton voltage multiplier and a sealed gas-filled neutron tube driven by dispenser cathode. Neutron burst shape in pulsed mode of neutron tube operation is measured with stroboscopic time spectrometry, implemented on scintillation detector, and modeled with Comsol Script 1.3 and Comsol Multiphysics 3.5. Modeling appears to be in good agreement with experimental results. Measured pulse rise and fall times are 110 ns and 100 ns respectively. & 2016 Elsevier B.V. All rights reserved.
Keywords: Neutron generators Ion sources Finite element modeling
1. Introduction A slim-shaped pulsed DD-neutron generator for science and industry is developed at Budker Institute of Nuclear Physics (BINP). The generator comprises Cockcroft–Walton voltage multiplier and gas-filled neutron tube. Penning-type ion sources are commonly used in neutron tubes for logging tools [1–5]. The basic distinction of neutron tube developed at BINP from the most of commercial gas-filled neutron tubes is utilization of a dispenser cathode ([6], barium dispenser cathode is heated indirectly by a filament, see Fig. 1) in ion source. This development is made in pursuit of short fronts of neutron bursts. One of the values, that characterize pulsed mode of operation of neutron generator, is a pulse rise and fall time, defined as time interval between the moments when neutron yield reaches 90% and 10% of maximum value. Particularly the pulse fall time is of great importance in pulsed neutron well logging technology (particularly, in inelastic gamma ray spectroscopy) [3]. Modern gas-filled neutron tubes with conventional Penning-type ion sources produce neutron bursts with rise time of 2 μs and fall time of about 1 μs [3,7]. The shape of neutron bursts is reported to be different among neutron generators of one type [8]. “Thermo scientific” company reports the best result – neutron generator P 385 with rise/fall time of 1.5/0.5 μs [9,10]. One of possible approaches to minimize the rise/fall time is utilization of dispenser cathode in ion source of neutron tube. This kind of neutron tube (called “Minitron”) was pioneered at n
Correspondence to: Lavrientev avenue, 11, Novosibirsk, Russia. E-mail address: [email protected] (E. Grishnyaev).
http://dx.doi.org/10.1016/j.nima.2016.05.021 0168-9002/& 2016 Elsevier B.V. All rights reserved.
Schlumberger company in 1991 [11] and successfully applied for pulsed neutron logging until now. “Minitron” is the first and the only commercial neutron tube with ion source driven by dispenser cathode. Schlumberger never discloses the details of engineering calculations involved in the process of equipment development, so, this work together with [12] are the first ones elucidating the approach to calculation-based development of compact neutron tube with ion source driven by dispenser cathode. Typically, the logging tools utilize DT-neutron generators. This paper presents the modeling results and benchmarking of the model performed on the DD neutron generator. The neutron burst shape evaluation using the DD neutron generator is driven by the safety considerations, while the main conclusions are applicable for DT generator.
2. General description of neutron tube A neutron tube consists of the ion source, gas source, accelerator column and a target. The target is made of the material that is saturated with deuterium prior to use of the neutron generator. The nuclear reaction takes place on the titanium target, when the accelerated deuterium ions collide with the deuterium atoms implanted in the titanium layer [13], resulting in the 2.45 MeV neutrons: Dþ D-3He(0.82 MeV) þn(2.45 MeV). Commercial sealed DD-neutron tubes produce 106 n/s with 50 μA of ion current and 80 kV of accelerating voltage [14]. The simplest case of a neutron tube for computer modeling is axially symmetric tube with ion source driven by dispenser cathode without magnetic field (Fig. 1). The principle of operation of this kind of tube is the following. Grounded cathode is placed close
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of getter heating current). Standard mode of neutron generator operation is 0.5 Pa of deuterium pressure, 10 mA electron emission current, pulsed 200 V anode voltage, 100 V extractor voltage, 50 μA ion current and 81 kV accelerating voltage.
3. The concept of plasmaless neutron tube As reported earlier [12], the tube can be thoroughly modeled with any modeling software based on finite element method (FEM) with particle tracing subroutine, provided electric field in ion source is high enough and space charge buildup does not lead to formation of potential extremums. Generally speaking, any modeling of deuterium-filled neutron tube should consider somehow all elementary processes (Table 1). Each process can affect distributions of electron and ion space charge densities in ion source and ion current density profile on target. Modeling, described in detail in [12] and in this paper, neglects influence of processes 1–3 on electron charge density distribution and processes 4–6 on ion charge density distribution. Validity of such simplification should be verified after completion of modeling. Estimation of probabilities for all neglected processes at nominal operating conditions gives the following results:
Fig. 1. Schematic representation of the neutron tube.
to the anode with a potential of about 200 V. The cathode uniformly emits electrons from its surface. Electrons accelerated with anode field traverse the inner volume of hollow anode until disappearing on electrodes (anode or extractor). Energetic electrons introduce ionization in the volume of ion source. Ions are extracted and directed to the target. Electrostatic field in two-electrodes ion optics, comprising the extractor and suppressor of secondary electrons, accelerates ions. The extractor is held under some constant voltage about 100 V to prevent ions from reaching the target after anode potential has switched to zero. The suppressor is connected directly to high voltage power supply. The target is connected to the suppressor through 8 MOhm resistor to make its potential less negative than suppressor potential during ion current flowing through the target. It prevents secondary electrons from leaving the vicinity of the target. The source of deuterium in the tube is a getter strip (we used St101 getter produced by SAES Getters [15]). Getter irreversibly adsorbs all gases except hydrogen isotopes, which are adsorbed reversibly. Equilibrium deuterium pressure in sealed volume of the tube depends on getter temperature, which is controlled with heating current. The higher the heating current, the higher the deuterium pressure. Ion beam current can be controlled in 2 ways: (1) changing of cathode emission current (through adjustment of cathode heating current), (2) changing of deuterium pressure (through adjustment
1. Total probability for electron to take part in the processes 1 or 2 or to undergo 1 “effective” elastic collision with D2 molecule is P123 ¼0.025 2. Ions in ion source are accelerated by more than 20 eV/mm. Under these conditions probability of D3 þ ion formation from D2 þ is below P4 ¼0.02. 3. Total probability for deuterium ion to undergo charge exchange or “effective” elastic (polarization) collision with D2 molecule in IS ion source is below P56 = 0.1 4. Mean total probability for deuterium ion to undergo charge exchange or “effective” elastic (polarization) collision with D2 tot molecule on its whole trajectory is P56 = 0.24 IS For self-consistent potential field estimation P56 is much more tot important than P56 , because potential field and space charge field are almost absolutely decoupled in ion optics (region of vacuum tot electrostatic field intensity about 27 kV/cm), but rather high P56 nevertheless means that exact replication of modeled ion current density on neutron generating target in real experiment cannot be expected. The degree of discrepancy between the modeled and experimentaly obtained current density profiles is still an object of experimental study. All probabilities, characterizing elementary processes in ion source, are shown to be low and self-consistent field can be simply modeled on the basis of freely moving particles tracing [12]. Our model includes only reactions of ionization (№1 in the Table 1). The absence of the irregularities in the electrical potential field in the ion source suggests that this ion source and entire tube can be referred to as plasmaless.
Table 1 Elementary processes taking place in DD-neutron tube. №. Elementary process 1 2 3 4 5 6
Dissociative ionization: D2 þ e-D þ þ Dþ 2e Nondissociative ionization: D2 þ e-D2 þ þ2e Inelastic scattering of electron on D2-molecules Elastic scattering of electrons on D2-molecules D2 þ þ D2-D3 þ þD Elastic scattering of ions on background D2 gas Charge exchange between ions and background D2 gas
Cross-section the sum of cross-sections for 200 eV electrons is 9 10 17 cm2 [16] total cross-section of D2-molecule excitation for 200 eV electrons is 2.9 10 16 cm2 [16] elastic scattering momentum transfer cross section for 200 eV electrons is 1.7 10 17 cm2 [17] cross-section reaches 10 14 cm2 at thermal ion energies and rapidly decreases at energies above 1 eV [18] described with momentum transfer cross-section of polarization interaction [19, 20] Cross-section data can be found in [19, 20]
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Plasmaless tube can be thoroughly modeled with stationary iterative method, described in [12]. In pulsed plasmaless mode (when voltage on anode is represented with square wave) transient process of ion current appearance and disappearance also can be thoroughly modeled.
4. Modeling of ion flow appearance The potential difference between the extractor and the anode is always 100 V (the sign of potential difference depends on current phase of anode square wave). So, the electric field is always strong enough to be considered as close to vacuum field (Fig. 2) and effects of space charge in the modeling of ion flow appearance are neglected. Another simplification follows from that electrons move more than 86 times faster than D2 þ ions (rough estimation of velocities ratio in the same electric field is mi = 4⋅1840 ≈ 86, me
but the fact that electrons are accelerated in the strongest field in “cathode–anode” region makes this ratio an estimation from below). Further treatment supposes that electron flow appears and disappears instantly. The approach to ion flow modeling is the same as in [12]: complete ion flow on the target consists of a set of current-bearing ion trajectories that start at the nodes of FEMmesh with nonzero ion birth rates. For every trajectory the timeof-flight is known from the particle tracing subroutine. The transient process is modeled in Comsol Multiphysics 3.5 and Comsol Script 1.3. The result of modeling is a sequence of time moments and according sequence of ion current values representing transient process. Consider the moment of time when rising front of square wave appears on the anode. This moment is represented by 2 values: time ¼0, current¼ 0. Each next column contains time-of-flight for trajectory and total ion current as cumulative sum of elementary ion currents. Columns are sorted by time in increasing order. Time profile of ion current appearance is shown on Fig. 4. One can see, that rather strong extracting field together with small size of ion source allows all ions to reach target in less than 150 ns for 90% of ions.
5. Modeling of ion flow disappearance When anode potential sharply switches from 200 V to zero electrons also disappear instantly as compared to ions. All ions, following those trajectories that end on target, can be divided onto 2 groups: (1) ions that have enough kinetic energy to overcome braking field and to be extracted to target, (2) ions that have not
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been accelerated enough to overcome braking field and disappear in ion source. Now every ion trajectory, modeled for 200 V at anode, is considered not as a stationary current-bearing streamline, but as a set of ions with different initial energies. These ions are aligned along the trajectory at initial time moment and reside at the points of trajectory discretization. The first task now is to figure out what ions can overcome braking field and what ions cannot. The second task is to estimate momentary values of currents carried by ions reaching the target. The correspondence of ions times-of-flight to momentary currents forms the waveform of particular streamline decay after anode voltage switches to 0. Every ion trajectory, modeled for the case of 200 V at anode, is analyzed this way. The example of this analysis is shown on Fig. 3. Modeling script starts from the first ion (that has zero kinetic energy) and checks if this ion reaches the target (see the set of solid trajectories ending inside the ion source in Fig. 3). If it does, the particle tracing subroutine estimates time-of-flight for this ion (see the last solid trajectory in Fig. 3. This trajectory leaves ion source and ends on target surface) and the script moves to the next ion along the trajectory and so on to the last point of a streamline. The result of streamline analyzing is a correspondence of a set of ions times-of-flight TOFt i (i is an index enumerating vertexes of a streamline corresponding to ions reaching the target) in “Off” field and a set of particle time values at streamline vertexes partTt i (this is the time counted from the origin of a streamline) in “On” field. One can estimate a waveform of a streamline current decay (set of decay
I i values at times
TOF
t i ) as
decay
Ii =
str
partT
I
t i + 1 − partTt i
TOF
t i + 1 −TOFt i
, where
str
I is a
stationary streamline current in “On” field. Examples of modeled waveforms are presented on Fig. 3. Every waveform has nearly flat part in the beginning. It corresponds to ions that traverse accelerating gap when anode voltage switches to 0 V. Decaying part corresponds to ions residing in ion source at the moment of switching. The time profile of total ion current decay is the sum of elementary current decay waveforms estimated for all streamlines (Fig. 4, right). One can see, that rather strong braking field together with small size of ion source allows only fast ions to reach target after anode voltage switches to 0 V. And it takes less than 150 ns for 90% of fast ions.
6. Measurement of neutron burst shape There are two possible approaches to study neutron burst
Fig. 2. Potential field in ion source of neutron tube with 200 V on anode (“On” field, left) and with 0 V on anode (“Off” field, right). Equipotential lines are shown in increments of 10 V.
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Fig. 3. Left: Example of D2 þ -ion trajectory analyzing. Thick dashed line is current bearing streamline modeled for 200 V at anode. Solid lines are ion trajectories modeled for 0 V at anode. For convenience of visual perception only the 1st trajectory reaching the target is shown. Right: 3 examples of modeled waveforms of elementary currents decay.
shape. The first (and the most obvious) one is to measure it directly with the method of time spectrometry (see, for example, [21]). The second way is to measure the waveform of ion current on target, bearing in mind that momentary value of ion current is proportional to momentary neutron yield. Ion current oscillography can explicitly approve or disprove repeatability of single pulses shape. And this is the apparent advantage of ion current oscillography over neutron output time spectrometry. But this advantage is valid only if one makes an extra effort to monitor the dynamics of secondary emission, beam spot size during ion source switching, stability of accelerating voltage during switching events and several other effects. Under these circumstances direct measurement of neutron pulse shape is significantly simpler and cheaper than ion current oscillography. To say nothing of the fact that only neutron time spectrometry can be considered as absolute proof that rise/fall time is equal to one value or another. Another argument in favor of time spectrometry is that pulse-to-pulse stability is not important in neutron technologies, because spectra of secondary particles (for example, scattered neutrons or characteristic γ-quanta in well-logging) are accumulated over many pulses and only integral neutron pulse shape really matters. So, time spectrometry is chosen to measure neutron burst shape. Scintillation neutron detector, developed earlier at BINP, is selected as major detector for fast neutron measurements [22]. Terphenyl crystal with dimensions ∅40 40 mm is used as a scintillator, photomultiplier (PMT) Hamamatsu R6231-100 is applied for scintillation flashes detection. Registration unit is
developed by BINP electronics group for PMT pulses analysis. The unit includes fast ADC and programmable logic array for preliminary pulses processing. ADC parameters are the following: counting rate 500 MHz, dynamic range 12 bit, memory 3 106 counts. These parameters are sufficient for direct measurement of stilbene scintillation pulse shape. It opens additional possibilities for neutron radiation analysis. Built-in programmable logic arrays algorithms are capable of real-time signal preprocessing and implementation of different modes of operation of the unit. Currently, the following operation modes of the unit are implemented: (1) oscilloscope mode for registration of input signals waveforms, (2) pulse shape registration mode (n-γ-discrimination) – for each scintillation pulse the 1 μs waveform portion is recorded, (3) count mode – the number of events for a given time interval is counted, (4) stroboscope mode with n-γ-discrimination – for each event a delay from reference pulse synchronized with anode pulse is stored in statistics. The last mode allows to measure temporal characteristics of a neutron flux.
7. Results and discussion The results obtained in the experiment on stroboscopic time spectrometry of pulsed neutron output together with fronts shapes predicted with modeling are shown at Fig. 4. One can
Fig. 4. Comparison of modeled waveforms of ion current appearance (left) and disappearance (right) with experiment. Solid lines are modeled waveforms. O-symbols represent time spectra of neutron bursts. Deviation bars are estimated as mean square deviation in Poisson's distribution (as square root of neutron yield).
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Fig. 5. Left: Modeled current decay waveforms for 2 extractor grids with different geometrical transparency: thick gray curve – L ¼ 0.65 mm, thin black curve – L ¼ 0.5 mm. Right: graphical explanation of how L is defined.
observe good agreement between modeling and experiment for the front edge of neutron burst, but there is some discernible difference between measured rear front and modeled one. Possible cause of this circumstance is the fact that ion current fall time depends on geometrical transparency of extractor grid (Fig. 5) while there is no such dependence for rise time. Indeed, “On” field accelerates ions and makes them traverse extractor grid rapidly [12]. Thus, rise time depends only on “macroscopic” geometrical characteristics of extractor grid (i.e., cone angle only) that define “far” field in the ion source (i.e. on the distances greater than L from the cone surface). “Off” field decelerates ions. It means that last streamline ions reaching the target (they correspond to decaying parts of elementary current waveforms, Fig. 3) spend a lot of time near the extractor grid (because of low initial energy) and their trajectories are strongly affected by detailed stricture of electrostatic field near the grid (“near” field), that is defined by “microscopic” geometrical characteristics of the grid (i.e. the value of L). See how last solid trajectory on Fig. 3 is distorted near the extractor grid. Thus, fall time depends not only on cone angle, but also on L. Real extractor grid, placed in the neutron tube, is made of square-celled grid with square side 0.5 mm and its shape is not ideally conical. Time delay between neutron yield reaching 10% and 90% of maximum (formal rule defining rise and fall time) is 110 ns for rise time and 100 ns for fall time.
8. Conclusion Neutron tube with ion source driven by dispenser cathode is developed at Budker Institute of Nuclear Physics. The tube is referred to as “plasmaless” tube, because extracting electric field in ion source is made high enough to extract ions rapidly, so space charge effects are of no significance in tube operation. Rise and fall times of neutron bursts, predicted with modeling in the frameworks of “plasmaless” approach, are in good agreement with experimental results of stroboscopic time spectrometry of pulsed neutron output. Measured rise and fall times are 110 ns and 100 ns accordingly. Neutron generator utilizing this tube is currently being exploited at BINP for calibration of cryogenic avalanche detector of weakly interacting particles. Another verification of plasmaless neutron tube operation theory is comparison of target erosion profile with modeled current density distribution. Of course, it can
be performed only after neutron tube malfunction.
Acknowledgments The development of modeling means was supported by Russian Science Foundation under grant N 14-50-00080. Manufacturing and activation of neutron tube and experimental measurement of neutron burst shape was supported by Russian Foundation for Basic Research under project No. 16-32-00042 mol_a.
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