1 Introduction

Nuclear fusion reactions are the most crucial reactions in nuclear astrophysics because they are responsible not only for powering stars but also for the synthesis of the elements in the universe [1, 2]. The ²H(d, p)³H fusion reaction plays a key role in the design of future fusion power plants and in the understanding of the primordial abundances in Big Bang nucleosynthesis models [3]. Therefore, this reaction has been studied using accelerators in the past several decades (see [4] and references therein). It is of particular interest to investigate reactions of this type when they are generated by high-intensity lasers in plasma environments that are similar to real astrophysical conditions. In recent years, with the rapid development of high-intensity laser technologies, it has become possible to produce this type of plasma environment in the laboratory [5-9].

Recently we have performed experimental investigations of the ²H(d, p)³H reaction using laser-driven counter-streaming collisionless plasmas at the Shenguang-II laser facility at the Shanghai Institute of Optics and Fine Mechanics of the Chinese Academy of Sciences. In these measurements, difficulties arise in the identification and quantification of the reaction products (such as electromagnetic pulses), which can interfere with electronic devices. To date, considerable effort has been made to develop detectors and investigate their performance for the study of laser-driven nuclear reactions, for example, the CR-39 and 4H-SiC detectors [10, 11]. We used CR-39 solid-state track detectors to record the energy and quantity of protons generated by the ²H(d, p)³H reaction. The CR-39 solid-state track detector [12, 13] is an ideal ion detector because it is sensitive mainly to ions but is insensitive to backgrounds such as electrons and photons [14]. When the ion energy is higher than 100 keV, the efficiency of the CR-39 solid-state track detector is nearly 100%. The energy threshold of CR-39 solid-state track detectors could be approximately 20 keV [14-16]. The performance of these detectors typically varies from batch to batch even when they are produced in the same factory [17]. Thus, one must calibrate each batch of CR-39 solid-state track detectors with monoenergetic protons like those used to study the ²H(d,p)³H fusion reaction. There are several requirements for the calibration of CR-39 solid-state track detectors. (1) It is necessary to avoid long-term exposure to air and ultraviolet radiation. (2) Because the particle track should be clearly identified, the beam current on the detectors needs to be less than 10⁵cm^-2. (3) In the calibration experiment, the beam of particles recorded by CR-39 solid-state track detectors should be monochromatic; because a proton beam with a large energy divergence is equivalent to a combination of protons of various energies, a detector calibrated by this method cannot accurately indicate the energy characteristics and track parameters of the detector. (4) In a single energy calibration experiment, multiple CR-39 solid-state track detectors need to be irradiated. There are several methods of irradiating CR-39 solid-state detectors with a proton beam produced by a traditional accelerator [14, 18-22] or a laser accelerator [23]. The Rutherford backscattering method [18, 19] and nuclear reaction method [20] are typical approaches using a traditional accelerator.

These pioneering results demonstrated that there is not a one-to-one correspondence between the proton energy and the track diameter in the energy region [14, 18, 19, 22, 23]. Consequently, there is an uncertainty when different proton energies are distinguished using their track diameters. Therefore, to analyze the ²H(d, p)³H reaction products recorded with a single batch of CR-39 detectors, research on methods of identifying the particle information is desirable.

In this work, we used a monoenergetic proton beam to irradiate a CR-39 detector, measured the dependence of the track diameter on the proton energy, and demonstrated a method of distinguishing different energies by considering both the track diameters and their gray levels. Note that in the laser-driven ²H(d, p)³H experiment, the energies of the incident deuterons are below 100 keV, and those of the outgoing protons and tritons are approximately 3 and 1 MeV, respectively. To stop deuterons and tritons, the CR-39 slices were coated with a 30–40 micron aluminum film. The proton energies were therefore reduced to approximately 2 MeV after the Al film. Thus, we used proton beams with energies ranging from 0.3 to 2.5 MeV for the calibrations.

2 Experiment

Proton beams with an intensity of approximately 20 pA and energies ranging from 0.3 to 2.5 MeV in 0.2 MeV steps were delivered by the GIC4117 tandem accelerator at Beijing Normal University. A schematic layout of the experimental setup is shown in Fig. 1. The protons are vertically incident onto the CR-39 detectors in the calibration because the CR-39 detectors are placed perpendicular to the direction of outgoing products in the laser-driven ²H(d, p)³H reaction experiment. The proton beam reaches the CR-39 detector through an aperture with a diameter of 1 cm and a slit with a width of 0.439 mm. CR-39 solid-state track detectors (Fukuvi Chemical Industry, Tokyo, Japan) are attached to a large rotating plate in a circular arrangement. The geometrical dimensions of each CR-39 solid-state track detector slice are 10 mm × 10 mm × 0.8 mm. In each measurement, the controllable target plate was rotated only once. We measured the time at which the laser passed through two adjacent holes using a He-Ne laser. The irradiation time on each CR-39 detector was deduced to be approximately 12.5 ms, as shown in Fig. 2. The proton irradiation of a CR-39 solid-state track detector can be estimated as

Fig. 1.Full-screen View

(Color online) Layout of experimental setup. The aperture has a diameter of 1 cm, and the slit has a width of 0.439 mm.

Fig. 2.Full-screen View

(Color online) (a) This irradiation duration was measured using a He-Ne laser, a photodiode (ET2000), and an oscilloscope. (b) The time interval between two holes 2.5 cm apart is approximately 30.69 ms. The irradiation time on each CR-39 detector was deduced to be approximately 12.5 ms.

where I is the current connected to the slit, t is the time of the CR-39 solid state track detector passing through the slit, Q is the charge of a proton, S₁ is the area of the aperture, and S₂ is the area of the slit. The proton number N per unit area of a CR-39 slice is approximately 5 × 10⁴, according to Eq. 1.

The CR-39 detectors should be chemically etched in an aqueous solution of NaOH or KOH at an appropriate concentration and temperature. In this experiment, the CR-39 solid-state track detectors were etched in a 6.5 mol/L NaOH solution and kept at a constant temperature of 70±0.1°C. After etching, we processed the CR-39 detectors in six steps, as shown in Fig. 3. Step 1: Wash the CR-39 detector in 700 mL of deionized water for 5 min to stop etching. Step 2: Wash the detector in 500 mL of deionized water for 5 min to clean it. Step 3: Wash the detector in 250 mL of dilute nitric acid (10%) for 5 min to neutralize alkaline substances. Step 4: Soak the detector in 600 mL of deionized water for 5 min. Step 5: Wash the detector in absolute ethanol (analytical purity) for 1 min. Step 6: Place it in a Petri dish, and place the detector and dish in a self-sealing bag.

Fig. 3.Full-screen View

(Color online) Post-processing of the CR-39 solid-state track detector.

After an appropriate chemical etching treatment, the damage trail (called a latent track) induced by the ionized particles in the CR-39 solid-state track detector can be visualized under an optical microscope. In this work, the track diameters of protons were measured using an automatic track image analyzer. First, the images from an optical microscope were acquired using a CCD camera. Then the analog pictures were converted to digital ones by an image acquisition card. Finally, the track diameters were measured using image processing.

3 Experimental results

In Fig. 4, we plot the dependence of the proton track diameter on the proton energy (0.3 to 2.5 MeV) after the detector was etched at 70°C in a 6.5 mol/L solution of NaOH for various etching times. An etching time of ≤20 h was suggested in our previous work [24]. The dotted lines in Fig. 4 are drawn as guides for the eyes. For the calibration curves corresponding to etching times longer than or equal to 8 h in Fig. 4, two proton energy values correspond to the same track diameter. Consequently, the energy cannot be determined using only the diameter. Fortunately, as shown in Fig. 5, the tracks for higher-energy protons are much darker than those for lower-energy protons. Thus, one can distinguish the proton energies by the gray levels of their tracks, even if the track diameters are identical.

Fig. 4.Full-screen View

(Color online) Track diameter vs. proton energy.

Fig. 5.Full-screen View

When the diameters are the same, the proton energy level can be distinguished according to the gray level of the track.

It should also be mentioned that the gray level along each track varies, and its distribution is not regular. This fact reflects the complex structure of the track, which makes the digitization of gray levels at high precision very difficult. Thus, we combined the quantitative analysis of the track diameters and the qualitative analysis of the gray levels to study the incident ions, which was proved to be an effective method of proton energy identification (Figs. 4 and 5).

4 Summary and Conclusion

In summary, we present new calibration results for CR-39 solid-state track detectors, which are widely employed as the main diagnostics in fusion reaction experiments and ion acceleration by superintense lasers, because they are sensitive mainly to ions but insensitive to backgrounds such as electrons and photons. We use a slit and a rotating plate to reduce the beam intensity. Using this method, we measure the dependence of the track diameter on the proton energy. The results suggest that it is difficult to determine the proton energy using only the track diameter. In this case, the energy of the reaction products can be obtained by combining a quantitative analysis of the track diameters and a qualitative analysis of the gray levels. The present results can be very helpful for analyzing the ²H(d, p)³H reaction products recorded with the same batch of CR-39 solid-state track detectors.