On the Application of Gas-Discharge Converters in Introscopy
Abstract Generated abstract
This article evaluates the use of gas-discharge converters, or spark chambers, as image-forming detectors for introscopy with ionizing radiation. It estimates key operating parameters under streamer-discharge assumptions, including achievable spatial resolution, light output, pulse-generator requirements, and photographic recording conditions. The calculations indicate that spark chambers can provide roughly 10 lines per millimeter resolution and sufficient luminous exposure for photographic documentation with suitable pulsed power and optics. Experimental images of test objects in a pulsed radiation field are presented as confirmation of the practical feasibility of the proposed approach.
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ON THE APPLICATION OF GAS-DISCHARGE CONVERTERS IN INTROSCOPY
V. I. Bystrov, V. D. Del, A. N. Dubov,
A. S. Kuleshov, V. K. Kuleshov
(Presented by the scientific seminar of the Research Institute of Nuclear Physics)
The choice of one or another method of inspection using ionizing radiation depends substantially on the method by which the energy of the ionizing radiation is converted into energy convenient from the standpoint of obtaining the information of interest.
Depending on the conditions of inspection of particular production processes or objects, the converters currently used as such include scintillation counters, X-ray screens, screens based on scintillating inorganic single crystals, radiographic films, xerographic screens, etc. Each of them has certain advantages, but practice imposes new requirements and, naturally, the need arises to create new systems satisfying these requirements.
At present one can speak with confidence about the application in introscopy of comparatively new converters, widely used in nuclear-physics experiments and known as gas-discharge converters (or, in generally accepted terminology, spark chambers).
The purpose of the present article is to discuss the fundamental possibilities of their application for visualizing changes in the fields of ionizing radiation created by various objects. As yet, the amount of information of this kind available in the domestic and foreign literature is limited [1, 2, 3, 4, 5]. It is mainly reduced to indicating the possibility of recording, with the aid of spark chambers (SC), large fluxes of charged particles, or to using them for studying the spatial parameters of charged-particle beams in accelerators.
Without going into the details of the operation of SCs, which are covered quite well in the sources cited above, let us make an approximate estimate of some of their parameters. In doing so, a number of questions naturally arise, namely: whether it is possible to provide the required operating modes of the chambers under conditions of continuous inspection; whether documentation of inspection results is possible; and whether one can obtain loading characteristics of the SC that are suitable from the standpoint of inspection.
Adopting the streamer mechanism of discharge development in the chamber, one may assert that, in the final analysis, the detectability of defects will be determined by the distance between neighboring streamers. Theory shows that a streamer may be regarded as an isolated region of excitation and ionization.
The radius of the streamer, determined by diffusion, is equal to [6]
\[ r_0=\left(6\int_{r_2}^{r_1}\frac{D}{V_-}\,dr\right)^{1/2}, \tag{1} \]
where
\(D\) — diffusion coefficient;
\(V_-\) — electron drift velocity;
\(r_1\) — the distance at which a single photoelectron is formed from the center of the charged sphere;
\(r_2\) — the lower limit of integration.
Under these conditions, per unit area of the chamber there can develop a number of streamers equal to
\[ M=\frac{1}{\left[2\left(6\int_{r_2}^{r_1}\frac{D}{V_-}\,dr\right)^{1/2}\right]^2}. \tag{2} \]
Taking \(r_0=3\cdot10^{-3}\) cm and assuming the distance between streamers to be \(\approx r_0\), we have
\[ M=10^4\ \text{streamers/cm}^2, \]
which corresponds approximately to a resolution of 10 lines per millimeter.
It is not difficult to determine the light flux from the IR under the conditions considered above.
Neglecting self-absorption in the gas and assuming that all excited atoms emit one photon each, we find the number of photons produced by a streamer. The number of excited atoms in the streamer during the time from \(t\) to \(t+dt\) is equal to [6]
\[ dn_{\phi}=n_e(t)\cdot P_{\mathrm{v}}\cdot p\cdot V_-\,dt, \tag{3} \]
where
\(n_e(t)\) — the number of electrons in the avalanche at time \(t\),
\(P_{\mathrm{v}}\) — the probability of excitation of an atom by an electron moving with drift velocity \(V_-\),
\(p\) — pressure, torr.
According to [8],
\[ P_{\mathrm{v}}=P_c\cdot h_{\mathrm{v}}=\frac{h_{\mathrm{v}}}{h_i}P_i =\frac{h_{\mathrm{v}}}{h_i}\frac{\alpha}{P}, \tag{4} \]
where
\(P_c\) — the probability of collision of an electron with a gas atom,
\(P_i\) — the probability of ionization of an atom upon collision with an electron,
\(h_{\mathrm{v}}\) — the efficiency of excitation of an atom,
\(h_i\) — the efficiency of ionization of an atom.
Substituting (4) into (3), we obtain
\[ dn_{\phi}=\frac{h_{\mathrm{v}}}{h_i}\,n_e(t)\cdot \alpha\cdot V_-\cdot dt. \tag{5} \]
Thus, the linear density of excited atoms along the track is equal to
\[ n_{\mathrm{v}}=\frac{dn_{\phi}}{dx} =\frac{dn_{\phi}}{V_-\,dt} =\frac{h_{\mathrm{v}}}{h_i}\,n_e(x)\cdot \alpha, \]
where \(x=V_-t\).
Since
\[ n_e(t)=n_0\frac{h_{\mathrm{v}}}{h_i}\exp(\alpha\cdot V_-t) =n_0\frac{h_{\mathrm{v}}}{h_i}\exp(\alpha x), \tag{6} \]
then integration of expression (5) gives
\[ n_{\phi}=n_{0}\frac{h_{B}}{h_{i}}\exp(\alpha\cdot V_{-}t_{i}) = n_{0}\frac{h_{B}}{h_{i}}\exp(\alpha\cdot l), \tag{7} \]
where \(t_{i}\) is the duration of the chamber supply pulse.
Under certain conditions [9], for example for neon, one can obtain
\[ n_{\phi}=8n_{0}\exp(\alpha\cdot l). \tag{8} \]
An estimate based on expression (8) shows that, at \(M=10^{4}\ \text{l}/\text{cm}^{2}\), \(4\cdot 10^{12}\) light photons are emitted from one square centimeter of the surface of the spark chamber.
To ensure such operating modes of spark chambers, it is not necessary to create any special conditions. As their power sources one may use generators of nanosecond high-voltage pulses, calculated according to the procedure described in [9, 10, 11, 12, 13]. Certain special features arise in cases where it is necessary to apply to the chamber, continuously over some period of time, a sequence of supply pulses. This is determined by the specific monitoring conditions. However, even in such cases there are no fundamental difficulties, and the technical side of these questions is quite solvable.
Let us consider several general requirements that must be met by the power sources of spark chambers.
The shape of the supply pulse for ordinary spark chambers is not of special importance: because they are simple to obtain, pulses with a steep leading edge and a gently sloping exponential decay are most often used. For streamer chambers, pulses having a shape closer to rectangular are required.
The amplitude of the pulses may vary within wide limits. In the general case it depends on the interelectrode gap of the chamber, the pressure, and the type of gas. Since, as a rule, the curve of the dependence of the efficiency of a spark chamber on the intensity of the applied electric field has a pronounced plateau of several kilovolts per centimeter, the requirements on the stability of the supply-pulse amplitude are not stringent.
The duration \(t_{i}\) of the voltage pulses for most spark chambers is about \(10^{-7}\) s. Streamer chambers operate normally with a pulse duration of \(10^{-8}\div 3\cdot 10^{-8}\) s.
The rise time of the supply pulse has a decisive influence on the operating efficiency of a spark chamber, since the initial part of the pulse acts like a clearing field. Therefore, if the leading edge is not sufficiently steep, there is a noticeable drift of electrons to the chamber electrodes, a decrease in their number in the gap and, consequently, a lowering of the efficiency of registration of ionizing particles.
The delay time of the chamber supply pulse relative to the moment when the particle passes through it affects the time resolution and the spatial density of the developed tracks and therefore must be optimal. Fulfillment of the latter requirement can be ensured by using special synchronization circuits. A typical equivalent circuit of a spark-chamber supply generator is shown in Fig. 1. The spark chamber itself is represented in the figure as a capacitance \(C_{K}\). A high-voltage thyratron or spark discharger may be used as the switching key \(K\). The resistance and inductance of the key and connecting leads are represented as elements \(R_{K}\) and \(L\). \(C_{n}\) is the storage capacitance; \(R_{n}\) is the resistance,
Fig. 1. Equivalent circuit of the SC power-supply generator
the shunting chamber; \(R_z\) is the charging resistance. For normal operation of the SC it is necessary that the following conditions be satisfied: \(C_n \gg C_k\) and \(R_z\) be sufficiently large.
Along with the requirements given above, no less important is the question connected with the procedure for taking information from the spark chamber. Without considering all methods of recording it, let us examine only the scheme for photographing the image from the chamber onto photographic film.
Assuming that the lifetime \(\tau\) of the excited states of atoms in the gas filling of the SC is much shorter than the observation time \(t_n\), and taking into account that the light emission of the atoms is isotropic, the light energy \(E\) emitted by each point of the streamer into unit solid angle is determined as
\[ E=\frac{n_B}{4\pi}\cdot \varepsilon_{\mathrm{sv}}\cdot \frac{1}{4\pi}\cdot \varepsilon_{\mathrm{sv}}\cdot \frac{h_B}{h_i}\cdot n_e(x)\cdot \alpha, \tag{9} \]
where \(\varepsilon_{\mathrm{sv}}\) is the energy of one light quantum, expressed in joules,
\[ \text{and } [E]=\frac{\mathrm{J}}{\mathrm{m}\cdot \mathrm{sr}}. \]
The photographing scheme is shown in Fig. 2, where
Fig. 2. Photographing scheme
\(1\) is the surface of the spark chamber from the side on which the image is taken; \(2\) is the camera lens; \(3\) is the surface of the photographic film, \(D_{\mathrm{in}}\) is the lens diaphragm.
To obtain high sensitivity, it is important that the diaphragm be as large as possible and the focal length as small as possible. Then the lens can be placed close to the surface of the spark chamber and thereby an increase in the light collection onto the photographic film can be achieved.
With a frame size of \(24 \times 36\ \mathrm{mm}^2\) and an SC area of the order of \(100 \times\)
for an area of \(100\ \mathrm{mm}^2\), the linear magnification \(m\) will reach approximately \(m \approx \frac{1}{3}\). In this case \(a = 4f\) and \(b = \frac{3}{4}f\), where \(f\) is the focal length of the lens.
Assuming that, in such a geometry, the diaphragm is “seen” from any point of the camera at one and the same angle, equal to
\[ \omega=\frac{\pi D_{\mathrm{in}}^{2}}{4a^{2}} =\frac{\pi D_{\mathrm{in}}^{2}}{64f^{2}} =\frac{\pi}{64}\varphi^{2}, \tag{10} \]
where
\[ \psi^{2}=\left(\frac{D_{\mathrm{in}}}{f}\right)^{2} \]
is the optical aperture of the lens, and taking the light-transmission coefficient of the lens to be equal to 0.5, we find the light energy \(E_0\) reaching the photographic film from each point of the streamer. It is equal to
\[ E_0 \approx 0.5\,E\cdot\omega . \tag{11} \]
From the entire streamer, the energy reaching the film is
\[ E_{\mathrm{total}}=\int_{0}^{l} E_0\,dx =0.5\omega\,\frac{\varepsilon_{\mathrm{sv}}}{4\pi}\, \frac{h_{\mathrm{v}}}{h_i}\,n_0\left(e^{\alpha l}-1\right), \tag{12} \]
where
\(l\) is the distance between the electrodes of the IC,
\(dx\) is an element of the streamer length.
Since \(\exp(\alpha\cdot l)\gg 1\), finally
\[ E_{\mathrm{total}} =0.5\omega\cdot\frac{\varepsilon_{\mathrm{sv}}}{4\pi}\, \frac{h_{\mathrm{v}}}{h_i}\,n_0 e^{\alpha l} \approx \frac{n_0\varepsilon_{\mathrm{sv}}\psi^{2}h_{\mathrm{v}}} {5\cdot 10\,h_i}\,e^{\alpha\cdot l}. \tag{13} \]
Taking the length of the streamer to be equal to \(l\) and taking into account that the depth of field of the lens is less than \(l\), one may assume that the image of the streamer is projected onto the photographic film in the form of a circle with radius
\[ r\approx m\cdot l\cdot \tan\beta = m\cdot l\cdot\frac{D_{\mathrm{in}}}{2a} \approx \frac{l\psi}{24}, \tag{14} \]
Then the exposure of a film region with area \(S\approx \pi r^2\) by one streamer will be
\[ E_{\mathrm{sv}_1}=\nu_{\lambda}\frac{E_{\mathrm{total}}}{S}, \tag{15} \]
where \(\nu_{\lambda}\) is the conversion coefficient for radiation with wavelength \(\lambda\) \([\mathrm{lm/W}]\), \([E_{\mathrm{sv}_1}]=\mathrm{lux\cdot s}\).
At a streamer density \(M\), a linear magnification \(m\approx \frac{1}{3}\), and element \(S\) on the film, over \(N\) supply pulses of the camera the exposure will be
\[ E_{\mathrm{sv}_N}=9E_{\mathrm{sv}_1}\cdot S\cdot M\cdot N\ [\mathrm{lux\cdot s}]. \tag{16} \]
Calculations made on the basis of the considerations given above show that, when using a “Yupiter-3” lens and high-sensitivity photographic films, it is possible to photograph the image of an object placed in the field of a standard pulsed ionizing-radiation source of the IRA-1D type in one (or more) pulse. This is confirmed by photographs of a lead ring and of several objects, presented in Figs. 3 and 4. The block diagram of the experiment is shown in Fig. 5.
Fig. 3. Image of a lead ring in a spark chamber
Fig. 4. Image of an aluminum strip with holes and other objects in a spark chamber
[In the diagram: “Synchronization circuit”; “Radiation source”; “Test object”; “Gas-discharge converter”; “Power generator for the gas-discharge converter.”]
Fig. 5. Block diagram of the experiment
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