1 INTRODUCTION

The reactions of cumulative particle production in interactions of protons and carbon nuclei with various nuclear targets are studied in the SPIN experiment. Cumulative reactions (or cumulative particles) are commonly referred to as the reactions of interaction between two nuclei in which particles are produced in the kinematic domain that is forbidden by the interactions of free nucleons. The study of the cumulative particle production with high transverse momenta is one of the ways to obtain information about the properties of nuclear matter. Based on the obtained data on the particle production at high transverse momenta, it was possible to draw interesting conclusions about the structure of nuclear matter [1–4].

The experimental setup is a single-arm, small-aperture spectrometer that is capable of capturing charged particles escaping from the target at angles of 25°−55° in a laboratory system. The setup is located on beamline 8, which has been designed to transport high-intensity beams extracted from the U-70 synchrotron, which is a part of the accelerator facility at the Institute for High Energy Physics (IHEP) [5]. The diagram of the setup is shown in Fig. 1.

Fig. 1.
figure 1

Diagram of the experimental SPIN setup at the U-70 accelerator: (1) vacuum pipe for particles ejected from the U‑70, (2) profilometers for measuring the position and profile of the extracted beam, (3) target station, (4) quadrupole lenses, (5) shutter, (6) dipole magnets, (7) radiation shielding (contour), (8) threshold Cherenkov counter, (9) trigger scintillation counters, (10) resistive plate chambers, (11) drift chambers, and (12) proportional chambers.

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The setup consists of a vacuum pipe for particles transported from U-70; secondary-emission chambers for measuring the position and profile of the extracted beam; a target station; quadrupole lenses; dipole magnets; radiation shielding; a threshold Cherenkov counter; trigger scintillation counters; resistive plate chambers; drift chambers; and proportional chambers. The spectrometer elements are located in two zones that are separated by radiation shielding. In the so-called “hot” zone, there are a target station, chambers for measuring the beam position and profile in front of the target, and a shutter. The six elements of the magnetic optics located in the hot zone can be tuned to select a particle escaping from the target with the desired momentum and angle. This particle is then guided to the “cold” zone through a hole in the radiation shielding. In the cold zone, where the background radiation level is several orders of magnitude lower than in the hot zone, the momentum is measured and the particles are identified. A description and characteristics of the main elements of the setup are presented in the next sections.

2 BEAM TRANSFER LINE

The particle beam extracted from the vacuum chamber of the accelerator into beamline 8 is used in the experiment. The beamline is designed so that proton beams with an intensity as high as 1013 particles can be transferred over a U-70 cycle. A powerful radiation shielding is required to ensure safety of the personnel at such intensities; it consists of steel slabs with a thickness of  ≥1 m, which are covered with concrete blocks with a thickness of  ≥2 m.

A cycle of the U-70 synchrotron has several phases: accumulation of the beam at a magnetic field in the ring magnet; acceleration with a ramp up of the magnetic field; a plateau on which the magnetic field is constant and the accelerated beam is supplied to consumers; and ramp down of the magnetic field. The duration of the synchrotron cycle varies from 8 to 11 s. The beam is delivered to the setup for 0.3−2.0 s per cycle, depending on the operating mode of the accelerator facility.

Several methods for ejecting the beam into beamline 8 have been implemented for the U-70 synchrotron [5, 6]:

1. extraction by means of crystal deflectors, using the effect of particle channeling in a bent crystal, which allows obtaining a beam with an intensity of 108−1010 particles per cycle uniformly during the plateau;

2. fast extraction using a kicker magnet, which allows a fixed number of bunches to be extracted into the channel per one turn of the beam in the accelerator;

3. slow resonant extraction and slow stochastic extraction, which allow particles to be uniformly extracted during the entire plateau of the accelerator’s magnetic cycle with an intensity of 109−1013 per cycle.

3 BEAM DIAGNOSTICS

The following parameters of the beam extracted into beamline 8 are continuously monitored during data acquisition at the SPIN setup:

1. the intensity in the range from 5 × 1010 to 5 × 1012 protons/cycle is measured using a secondary emission chamber (SEC) [7], which is located at the beginning of the beamline 8;

2. the position and profile of the beam both in front of and after the setup target are measured in the specified intensity range by means of two–coordinate profilometers (16 channels per plane; electrode pitch, 2.5 mm; surface thickness, 10 mg/cm2) that are equipped with high-sensitivity electronics; the mode of multiple measurement of the proton-beam profile is also possible (up to 16 measurements during extraction).

3.1 Secondary Emission Chamber

The chamber’s operation principle consists in measuring the positive charge produced on a thin metal foil (Ti, 30 µm) by electron emission from its surface when a proton beam passes through it. The secondary electron emission coefficient in the energy range of the primary beam of more than 1 GeV depends only slightly on its energy. At the same time, there is a strong dependence of this coefficient on the state of the surface, so the emitter foils are carefully cleaned. For the stable operation of the chamber to be ensured, the ambient gas pressure must be below 10−5 Torr (in our case, an independent magnetic-discharge pump is used). At the same time, the ionization component of the output current does not exceed several tenths of a percent of the secondary electron-emission current. On both sides of the plane of the emitter foil (the cathode) there are 15-µm-thick aluminum collector foils (the anode) kept at a positive potential of more than 100 V. This corresponds to the initial part of the plateau in the volt−ampere characteristic of the chamber.

The advantages of the technology for measuring the intensity using the SEC include its high speed and its linear response in a wide range of beam intensities, which are many times higher than the intensities of the operating accelerators. A combination of three consecutive emitters is used to increase the signal produced. The amount of substance introduced into the beam is approximately 40 mg/cm2. This chamber remains operable until the flux exceeds 1019 protons/cm2 according to experimental estimates.

3.2 Data-Acquisition Electronics

Specialized current integrators are used to measure the charge from the SEC. The minimum current value is at a level of tens of picoamperes; therefore, the integrator and the corresponding electronic components must provide measurements of low currents with a high accuracy. Unlike the conventional analog integrators based on operational amplifiers, the charge is measured here by means of digital integration. The integrated current is converted into the pulse repetition frequency. The number of pulses in the selected time interval is uniquely related to the integral of the input current over the same time, i.e., is proportional to the measured charge. The measurement accuracy is determined by the frequency of the quartz-crystal oscillator and the precision resistor. This allows easy change of the scale and guarantees high accuracy. In addition, the increase in the integration time here is not accompanied by an increase in the error inherent in the analog integrator. The duration of integration is determined only by the capacity of the pulse counter. Multiple measurement of the intensity during beam extraction is carried out by multiple interrogation of the counter. This allows recording of the time structure of a spill at a frequency as high as 600 Hz.

3.3 Calibration and Uncertainty

The long-term practice of SEC application at all large accelerators in the world provided accumulation of extensive experimental material that helped to determine the value of the secondary electron emission coefficient for most metals at different beam energies. However, as already noted, the accuracy of these data is estimated at 15% due to the strong influence of the state of the emitter surface on the value of this coefficient. Bench calibration is fraught with great difficulties. Therefore, the accuracy in measuring the absolute intensity of the extracted beam can be improved by calibrating the SEC using more accurate instruments with the same beam. In our case, this problem is easily solved by using a current transformer that measures the intensity of a fast extracted beam. The beam paths during both slow and fast extraction coincide at the sites of the SEC setup and current transformer. The latter is easily calibrated using a reference electric charge with an accuracy of 0.1%, and this calibration can be carried out at any time during a U-70 run. Due to the high speed, the integral SEC responses are proportional only to the intensity, regardless of the beam duration. This offers a chance to calibrate the chamber during fast extraction against the current transformer that provides an absolute accuracy of 2% or better over the entire operating range. For the saturation of the current-to-frequency converter to be avoided during fast extraction, an expansion circuit with a time constant of 20 ms is placed at its input; this circuit is switched off for the slow extraction. The procedure is repeated twice in each run since the secondary electron emission coefficient slowly changes as the integral dose increases. Analysis of the results of multiple calibrations carried out over the past few years makes it possible to determine the uncertainty for the SEC of channel 8, taking into account the actual background conditions at a level of 4% or better at intensities above 109 protons/cycle.

3.4 Beam Profilometers

The geometric dimensions and position of the extracted beam are determined using multielectrode detectors (profilometers), which are installed in the beam line at a distance of 89.4 cm before of the target and at a distance of 935.8 cm after the target. The signal from each electrode is generated by secondary electron emission, as is the case of the SEC. Two-coordinate assemblies with 2.5-mm-wide electrode strips are used. The pitch of the electrodes is selected so that the beam width at the level of four standard deviations fits into 6–8 channels. The width of the sensitive region is 40 mm. The electrodes are made of a 12-µm-thick polyamide film, which is glued to a textolite frame and on which aluminum is then applied by vacuum deposition. The interelectrode distance between the anode and the cathode is 6.5 mm. The high radiation hardness of the film (tens of thousands of megarads) and the small amount of substance introduced into the beam allow the profilometers to be used in the beam without replacement during several runs.

4 TARGET STATION

The automated target station is a mobile platform (Fig. 2) on which samples used as targets in the SPIN experiment are placed in the beam. The platform is capable of precisely moving the samples in a horizontal plane along and across the beam direction. A cassette with nuclear targets and a liquid-hydrogen target (LHT) are installed on the platform. Depending on the tasks of the experiment, either a nuclear target or the LHT can be introduced in the beam. The positioning accuracy is 0.2 mm.

Fig. 2.
figure 2

Target station of the SPIN setup: (1) cassette for nuclear targets and (2) liquid-hydrogen target.

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The station is equipped with a telemechanics system for remote control of the cassette and control of the movement. The movement and the cassette are controlled by commands coming from a computer that is responsible for slow control. Commands are transmitted via a communication line based on the RS-485 data-transmission protocol to a specialized control unit manufactured by OOO Avtomatika (Protvino, Moscow oblast, Russia) [8], which is located behind the shielding at a distance of 6 m from the target station. The logical protocol for communication between the computer and the unit complies with the GOST IEC 61107-2011 interstate state standard.

4.1 Nuclear Targets

Nuclear targets are thin plates of tested materials, e.g., tungsten, copper, aluminum, and carbon. Thin targets are understood to be targets for which corrections for the interaction of secondary particles in the target material are negligible. A set of nuclear targets is fixed on a disk-shaped cassette. A needed target can be put in the beamline by rotating the disk. There are six target sites on the disk. One of these is left free for making control measurements with an “empty target.” The automated system ensures replacement of targets without stopping the beam ejection to the setup. The typical time required for the replacement is approximately 15 s, which makes it possible to obtain data for different targets at the same beam parameters. If a target set must be changed, the target cassette is replaced manually after beam interruption within no more than 5 min. As an example, Table 1 shows the characteristics of the targets of one of the sets used for the data acquisition.

Table 1. Nuclear targets used in the data acquisition in 2015 at the SPIN setup
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4.2 Liquid-Hydrogen Target

The liquid-hydrogen target (Fig. 3) is capable of liquefying hydrogen or deuterium in a condenser cooled with liquid helium and confining it in the working volume in a thermally stabilized state at a beam intensity as high as 1012 protons per U-70 cycle. This is achieved by the reliquefaction of evaporating hydrogen (deuterium) at a constant pressure in the refrigerator mode of operation of the cryostat.

 Geometric parameters of the target:

 

 length of the working volume with hydrogen, mm

140

 diameter of the working volume with hydrogen, mm

40

 thickness of flanges, µm:

 

 of working volume with hydrogen

50

(stainless steel)

 of vacuum volume

100

(aluminum)

Fig. 3.
figure 3

Diagram of the liquid–hydrogen target.

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Figure 4 shows the time dependences of the liquid-helium flow rate and the target temperature since the start of the target liquefaction.

Fig. 4.
figure 4

Graphs for the LHT reaching the operating conditions: (a) flow rate of liquid helium and (b) the temperature inside the working volume with hydrogen. Time t = 0 corresponds to the beginning of LHT cooling.

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The graphs in Fig. 4 show that the operating mode is reached approximately 4−5 h after the start of the work with the LHT. The helium consumption in the normal operating mode is of the order of 30 L/day. The experience gained in operating the LHT shows that one 200-L Dewar vessel filled with liquid helium is enough for continuous 7-day operation of the target, excluding the helium consumption for the precooling.

5 MAGNETO-OPTICAL ELEMENTS

The SPIN experiment is aimed at studying cumulative processes in the region of large transverse momenta. The cross sections of reactions in this region are only a few nanobarns. In order to detect such a rare event, a beam with an intensity of up to 1013 protons per U-70 cycle is ejected to the experiment target. Because of high radiation doses, it is impossible to place detectors and electronics in close proximity to the target inside the radiation shielding of the beamline. (For reference: approximately 1010 interactions happen in 1 s of the U-70 burst if the target thickness is 0.1% of the nuclear length. This value is greater relative to the LHC: 40 MHz × 27 interactions per intersection of bunches, or ~109 s−1, and is closer to HL-LHC: 127 interactions per intersection of bunches [9].) Magneto-optical elements (MOE) are used to solve this problem. They allow secondary charged particles produced in the target to be transported through a hole in the shielding, which is located at an angle of 30° relative to the beam.

Figure 1 shows the layout of the MOE. Inside the radiation shielding are two pairs of 20K100B quadrupole lenses (4) Q1, Q2 and Q3, Q4 [10] and two dipole magnets: an SP12A magnet M1 and a C-shaped SP92 magnet M2 [11]. The spectrometric part of the setup with an analyzing SP12A dipole magnet M3 is located outside the shielding. The main parameters of the magnetic elements are presented in Table 2. The value of the maximum field at the center of the dipole magnet or at the pole of the quadrupole lens is also presented in Table 2. This value is limited either by design features or by the power source that is connected to the element.

Table 2

Magneto-optical elements

Aperture width (diameter), mm

Aperture height, mm

Yoke length, mm

Maximum available field, T (gradient, T/m)

20K100B (Q1−Q4)

200

−

1000

1.3635

SP12A (М1)

500

200

3000

1.4768

SP92 (М2)

230

110

1500

1.6975

SP12A (М3)

200

500

3000

1.5493

The magnetic elements inside the shielding are mounted on stands that can move along the rails. By moving the MOE, it is possible to select the angle at which secondary particles escaping from the target are transported to the spectrometric part of the setup through the hole in the radiation shielding. The MOE is installed in the required position manually under the supervision of the geodetic service. The movement mechanics allows selection of angles in the range of 22°−54.94° with the beam direction. The MOE are positioned with an accuracy of approximately 3 mm for the linear displacement of the M1 magnet and better than 1 mrad for the angular movement of the lenses. The geometric constraints brought about by the optimization of particle acceptance by the MOE system are such that the C-shaped magnet M2 must be moved linearly and rotated around a vertical axis. The accuracy of the M2 positioning during linear and angular displacements is 2 mm and 2 mrad, respectively.

The momentum of transported particles can be set by changing the MOE current. The geometrical parameters of the aperture and the maximum available field of the magnetic dipoles impose restrictions on the momentum of charged particles that can be transferred outside the shielding. Figure 5 shows the limits on the momentum of the transferred particles as a function of the angle to which the MOE is tuned. The momenta of particles flying out into the spectrometer aperture for elastic scattering are shown for reference.

Fig. 5.
figure 5

Restrictions imposed by the magnetic elements on the maximum particle momentum that can be ejected outside the radiation shielding depending on the MOE setting angle (solid line); the restriction on the particle momentums flying into the spectrometer aperture for the elastic proton scattering reaction is shown for reference (dotted line).

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The region of beam interaction with the target that is visible by the setup depends on the angle to which the spectrometer is tuned. Figure 6 shows the size of the particle acceptance area downstream of the beam as a function of the angle at which the SPIN spectrometer is tuned. The target positions relative to the zero point of the setup are also shown in Fig. 6; this parameter is important for work with the LHT.

Fig. 6.
figure 6

Dimensions of the visible interaction region vs. the angle at which the SPIN spectrometer is tuned.

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The acceptance region at all angles of MOE setting is such that particles are incident on the spectrometer both from the LHT working volume and from the flanges limiting the hydrogen and vacuum volumes. This fact must be taken into account when making measurements.

The adjustment of the recoil arm to a certain (“central”) momentum P and recoil angle α is performed on the basis of Monte Carlo calculations. The calculations use the momentum spectrum of protons from the target at a fixed angle. This spectrum is taken either from available models (URQMD, FRITIOF, etc.) or from our data for another angle. The MOE locations in the hot zone and the currents in all magnetic elements are selected to meet the following conditions:

1. the mean momentum at the exit from the setup is equal to P;

2. the mean values of the polar (θ) and azimuthal (φ) angles of particle acceptance are equal to the specified recoil angle and zero, respectively;

3. the mean values of the angles θ and φ should not depend on the selected momentum in the recoil arm;

4. the width of the angular distributions should not depend on the measured recoil momentum and the displacements of the incident proton beam within ±1 and ±0.5 cm in the horizontal and vertical directions, respectively, from the axis of beamline 8;

5. when the conditions 1−4 are met, the maximum angular acceptance (Δθ, Δφ) is attained.

An example of the Monte Carlo calculation of MOE settings for an angle of 40° at different values of the central momentum equal 4 GeV/c is shown in Fig. 7.

Fig. 7.
figure 7

Acceptance of secondary particles vs. the angle and the momentum at an angle of 40° (the Monte Carlo calculation).

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At a specified angle to which the MOE are tuned, experimental data are collected at different values of the central momentum P. Tuning to the desired central momentum requires that certain regimes of all magnetic elements be set. The tuning is performed automatically by accessing the technological database. It contains information about the value of the current in each magnetic element of the IHEP accelerator facility. A record into the corresponding fields of the technological database acts as a signal for changing the regime of a magnetic element. In the process of data taking, the data-acquisition system of the SPIN setup “reads” the technological database after each U-70 cycle and monitors the regimes of all MOE.

6 SHUTTER

When the yields of charged particles are measured, the spectrometer of the setup is hit by background particles, which are produced not in the target but in other structural elements of the beamline (e.g., in the flanges of the evacuated ion pipe). In addition, it is possible for particles produced in the target to penetrate outside the path determined by the MOE. For the contribution of background particles to be taken into account, three additional measurements must be performed both with an empty target and with a shut aperture of the MOE channel:

1. A measurement with an open MOE channel and a removed target (NO−TGT) determines the background from particles that were generated on the structural elements of the channel and penetrated into the spectrometric part of the setup both along the MOE channel of the hot zone and directly through the hole in the biological shielding.

2. A measurement with the MOE channel closed by the shutter and with the introduced target (BGR) determines the background from particles that were produced both on the target and on the structural elements of the channel and penetrated into the spectrometric part of the setup through the hole in the biological shielding, bypassing the MOE channel.

3. A measurement with the MOE channel closed by the shutter and with the target removed (BGR−NO−TGT) determines the background from particles that were produced on the structural elements of the channel and penetrated into the spectrometric part of the setup, bypassing the MOE channel.

The normalized background yield is

$${{Y}_{{BGR}}} = \frac{{{\text{|}}\text{NO}{\kern 1pt} - {\kern 1pt} \text{TGT}{\text{|}}}}{{{{N}_{{1p}}}}} + \frac{{{\text{|}}\text{BGR}{\text{|}}}}{{{{N}_{{2p}}}}} - \frac{{{\text{|}}\text{BGR}{\kern 1pt} - {\kern 1pt} \text{NO}{\kern 1pt} - {\kern 1pt} \text{TGT}{\text{|}}}}{{{{N}_{{3p}}}}}.$$
(1)

Each term is normalized to the corresponding number of protons Nip that hit the target during the measurement (index i denotes the respective measurement).

A shutter covering the aperture of the second lens is placed in the gap between the quadrupole lenses Q1 and Q2 to allow making these measurements. The shutter is a steel cylinder with a diameter of 20 cm and a length of 50 cm. The shutter is equipped with a position control system (introduced/removed) and is controlled remotely in the automatic mode using the same unit as the target station.

7 ANALYZING PART OF THE SPIN SETUP

Measurements of the flux of secondary particles, their identification, and momentum measurement are performed in the analyzing part of the SPIN setup, which is located outside the radiation shielding of beamline 8 in the so-called cold zone. The location of the spectrometer detectors is schematically shown in Fig. 8. A threshold Cherenkov counter resides in the hole in the biological shielding. Behind it there are a resistive plate chamber that generates the Start signal for the time-of-flight system, trigger scintillation counters, three stations of drift chambers, a spectrometric magnet, two stations of proportional chambers, trigger scintillation counters, and a resistive plate chamber that generates the Stop signal for the time-of-flight system.

Fig. 8.
figure 8

Layout of the equipment in the spectrometric part of the SPIN setup. The radiation shielding is shown as a contour.

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7.1 Threshold Cherenkov Counter

The threshold Cherenkov detector and the time-of-flight system are used for particle identification. The resolution of the time-of-flight system makes it impossible to reliable discriminate between π and K mesons with momenta greater than 2.5 GeV/c. The signal from the Cherenkov counter is used to do this. The counter consists of a radiator, a spherical mirror, and an XP2041Q photomultiplier tube (PMT) with a quartz window. All PMT dynodes and cathode are powered by a Walton−Cockcroft generator that is located on its base. The design of the counter is schematically shown in Fig. 9. The entrance window of the radiator is located inside the hole in the radiation shielding. The mounts of the mirror and the PMT protrude outward, which provides ease of adjustment and maintenance. The windows are made of 100-µm-thick aluminum foil.

Fig. 9.
figure 9

Diagram of the threshold Cherenkov counter.

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The detection threshold for π-mesons is 2.2 GeV/c. It was selected based on the capabilities of the time-of-flight system. Octafluorocyclobutane (C4F8) with refractive index n = 1.00130 at normal pressure (e.g., see [12]) was chosen as the working gas for the Cherenkov detector. The dependence of the quantity n−1 on the pressure was also presented in [12]. The gas is held at a pressure of 1.7 atm. The length of the gas gap is approximately 5 m. The calculated number of Cherenkov photons from a 1-m-long path in the wavelength range of 350−500 nm is shown in Fig. 10 as a function of the momentum for charged π and K mesons. As follows from these calculations, the Cherenkov detector filled with gas at the selected pressure should provide reliable discrimination between π and K mesons in the momentum range of 2.5−5.6 GeV/c.

Fig. 10.
figure 10

(a) Calculated numbers of photons for π mesons (circles) and К mesons (squares) during the passage of 1-m-long gas radiator and (b) measured efficiency of the Cherenkov detector in identifying π mesons and the probability of false triggering.

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The efficiency of the Cherenkov detector at different momenta was determined as the probability of the detector being triggered when a π meson passed over the spectrometer arm. When the spectrometer is tuned to detect negatively charged particles, the fraction of π− mesons among particles with a momentum p < 3 GeV/c is the main one, according to the data from the time-of-flight system, which makes it possible to measure the efficiency of the Cherenkov detector. The measured values of the detection efficiency for π mesons are shown in Fig. 10b (curve 1). At momenta above 2.5 GeV/c, the Cherenkov detector identifies charged π mesons with an efficiency of 97−98%.

Due to the limited space in the cold zone, the major part of the radiator was inserted into the hole in the radiation shielding. The Cherenkov detector, placed in this way, turned out to be sensitive to the fluxes of background particles flying out of the “hot” zone bypassing the MOE channel. The probability of false triggering of the Cherenkov detector due to loading by background fluxes is shown in Fig. 10b (curve 2). The probability of accidental triggering does not depend on the momentum and may vary in the range of 2−5% depending on the beam intensity and the type of the target inserted into the beam.

7.2 Scintillation Counters

There are six scintillation counters in the cold zone, two of which are located before of the spectrometric magnet and four are located after this magnet. When the signals from all these counters coincide, a trigger is generated to start the data-acquisition system of the SPIN setup. The efficiency of the trigger system consisting of six scintillation counters is continuously monitored in a special exposure, and its value is approximately 88.5%.

The counters are made from plates of polystyrene doped with 1.4-di(5-phenyl-2-oxazolyl)benzene (POPOP) and p-terphenyl. The sensitive area of the two counters in front of the M3 magnet, which is 200 × 200 mm, correspond to the dimensions of the hole in the radiation shielding. The thickness of the plates is 5 mm. The aperture trigger counter after the M3 magnet has dimensions of 505 × 310 mm.

8 TIME-OF-FLIGHT SYSTEM

The time-of-flight system consists of two detectors. Both detectors are multigap resistive plate chambers (MRPCs). The MRPC1 detector provides the initial time stamp when a particle passes through it and is located at the exit from the hot zone of the setup after the Cherenkov detector. The MRPC2 detector provides a time stamp when the particle leaves the setup and is located ahead of the final trigger counter. The distance between these detectors is ~12 m.

Both chambers have the same design, which is schematically shown in Fig. 11. The MRPC1 and MRPC2 chambers consist of 12 and ten independent gas gaps, respectively. A constant operating voltage of 1.75 kV is applied to each of them. The gas gap is formed by two 0.55-mm-thick glasses. The gas gap value of 0.25 mm is provided by spacers made of a fishing line. The glasses that make up the MRPC were manufactured by Glaverbel (St. Petersburg, Russia). The gas mixture for the MRPCs consists of tetrafluoroethane (C2H2F4), sulfur hexafluoride (SF6), and isobutane in a ratio of 90 : 5 : 5 vol %.

Fig. 11.
figure 11

Diagram of the MRPC: (1) high-voltage coating, (2) glass electrode, (3) spacer, (4) insulating layer (Mylar), (5) signal electrode, (HV) high-voltage source. Wavy lines indicate the missing gas gaps at the top and bottom.

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The plane with the signal electrodes (strips) is located in the middle of the chamber so that there are six and five gas gaps in MRPC1 and MRPC2, respectively, on both sides of it. The strips in MRPC1 and MRPC2 have dimensions of 25 × 210 and 25 × 310 mm, respectively. The pitch of the strips is 26.5 mm. The number of strips is eight in MRPC1 and 16 in MRPC2. The active detection zone (width × height) in MRPC1 and MRPC2 is 200 × 212 and 300 × 424 mm, respectively.

The background occupancy of MRPC1 is 2−3 kHz/cm2 per spill; for MRPC2, it is approximately 100 Hz/cm2. To get a high rate capability, MRPC1 is added with a heating system [13]. The operating temperature of MRPC1 is maintained at a level of 27 ± 0.5°C. These temperature conditions are provided by a temperature controller using two heaters located on the surfaces of the chamber caps. The MRPC1 chamber, together with the heaters, is covered with a heat-insulating material for the thermal stabilization. There is no need for such a heating system for MRPC2.

MRPCs are equipped with an amplifier−discriminator based on a NINO chip [14], which was developed for the ALICE experiment. The output signals of the amplifier−discriminator are transformed into ECL levels by the LVDS−ECL converter. The ECL signals are then transmitted via a 5E-category twisted pair to the time-to-digital converter (TDC) modules in the experimental house. The length of cables from MRPC1 and MRPC2 to the TDC modules is 25 and 12 m, respectively. The TDC modules of the VX1290A model are used, which have a resolution time of 25 ps [15]. The resolution of the front-end electronics channel together with the TDC channel is 22 ps.

The Time over Threshold method is used to obtain an accurate time stamp from the MRPCs. To do this, the TDC registers the arrival times of the leading and trailing edges of the MRPC signal. The dependence of the arrival time of the leading edge on the signal width is determined from the experimental data of the spectrometer, which is tuned to measure negatively charged hadrons with a momentum of 2 GeV/c. Such data contain a small (approximately 1%) number of K mesons and antiprotons, which does not complicate the detection of the desired dependence. The width of the momentum acceptance of the spectrometer (approximately 5%) provides a small blurring of the flight time of pions (approximately 60 ps). A description of the procedure used can be found in [16]. In the session of 2020, the total time resolution of the time-of-flight system was 86 ps (Fig. 12).

Fig. 12.
figure 12

Time-of-flight distributions in different runs at the SPIN setup: (a) for negative π− mesons at a momentum of 2 GeV/c (data obtained in 2020), the dashed curve is the fit by the normal distribution function with a standard deviation of 86 ps; (b) for negative particles at a momentum of 2.8 GeV/c, provided that there was no signal in the Cherenkov counter (data obtained in 2020); and (c) for positive particles at a momentum of 4.2 GeV/c (data obtained in 2018), the time resolution is 120 ps.

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Figure 12a shows the time-of-flight distribution for negative π− mesons at a momentum of 2 GeV/c, which was obtained in 2020. The dotted curve corresponds to the fit of the normal distribution function with a standard deviation of 86 ps. Figure 12b shows the time-of-flight distribution of negative particles with a momentum of 2.8 GeV/c, provided that there was no signal in the Cherenkov counter (data of 2020). Peaks are visible in the distribution (from left to right), which correspond to π mesons, K mesons, and antiprotons. The presence of π mesons on this distribution was caused by the inefficiency of the Cherenkov counter. Figure 12b shows the time-of-flight distribution for positive particles with a momentum of 4.2 GeV/c. These data were obtained in 2018, and the time resolution was 120 ps. The data of the SPIN experiment, which were published before 2021, were obtained at this resolution.

9 TRACKING SYSTEM

A spectrometer consisting of an SP12A analyzing magnet M3 and a tracking system based on multiwire chambers is used at the SPIN setup to measure the momentum of secondary particles transported beyond the radiation shielding. There are three stations of drift chambers in front of the magnet and two stations of proportional chambers behind the magnet.

The tracking system is used to reconstruct the particle momentum with an accuracy of 0.4%. The measured particle track consists of two parts determined before and past the M3 magnet. The GRKUTA program from the GEANT 3.21 package is used to determine the momentum. Using this program and the magnetic field map, the track past the M3 magnet is reconstructed in the opposite direction so as to pass through the start and end points of the first part of the track (before the magnet). Therefore, two limit momentum values are obtained for each track, which provide an average value and error estimates.

9.1 Drift Chambers

The particle trajectory at the entrance to the analyzing magnet is determined using the drift chambers. Each chamber contains 32 anode wires. The pitch of the anode wires is 6 mm, and their diameter is 50 µm. Separating wires kept at the cathode potential are placed between the anode wires. The sensitive area is 19.2 × 19 cm2. The cathode planes are made of metallized Mylar and are separated from the plane of the anode wires by 3 mm. The chambers are arranged in three modules. Each module contains two X planes and two Y planes, 12 planes in total. To resolve the left-right ambiguity of the track position relative to the anode wire, the paired X and Y planes in each module are offset relative to each other by 3 mm along the X and Y axes, respectively. The maximum distance between the extreme drift chambers is 191 cm.

The drift chambers use a gas mixture consisting of argon and isobutane in a ratio of  70 : 30. The operating voltage for such a mixture is 1.95 kV. At this voltage, the maximum drift time is 63 ns, and the coordinate resolution of the drift chamber is 0.12 mm.

A UPD-16 amplifier−discriminator manufactured by the IHEP with a threshold of 2.5 µA is used as the on-chamber electronics. The ECL output signals of the amplifier−discriminator are transmitted via a twisted pair cable to the LE-84 time-to-digital converter, which is made in the MISS standard [16]. The module is based on an HPTDC chip [17].

9.2 Multiwire Proportional Chambers

The multiwire proportional chambers (MWPCs) [18], together with the drift chambers, are designed to reconstruct tracks of charged particles and measure their momenta by the deflection in the magnetic field of the spectrometric magnet M3. Seven chambers are installed behind the M3 magnet on the base of 2.3 m between the two modules: four small (400 × 520 mm) MWPCs and three large (900 × 1400 mm) MWPCs, in which only part of the wires are used. All chambers were manufactured using the same technology. The diameter of the anode wires is 20 µm, the pitch of the anode wires is 2 mm, and the anode–cathode gap is 5 mm. The relative error of momentum measurements in such geometry is less than 0.5%.

The inclination of the anode wires in MWPC-U and MWPC-V chambers to the horizontal plane is 10.8°; these chambers are rotated within 180° relative to each other around the vertical axis.

A three-component gas mixture of 70% argon + 29.5% isobutane + 0.5% dichlorodifluoromethane is sequentially fed into the chambers in two paths: in MWPC1–MWPC4 with a flow rate of 100 mL/min and in MWPC5−MWPC7 with a flow rate of 200 mL/min. The plateau of the charged-particle detection efficiency for this gas mixture begins at a voltage of 4600 V.

The information from the MWPCs is read out by on-chamber electronics [19]. The signals from the RPK-32 shaping amplifiers with an adjustable sensitivity threshold are combined into two branches for even and odd numbers of MWPC wires and are fed to the BR-RPK controllers of the data-acquisition system.

10 ALGORITHM FOR CALCULATING DIFFERENTIAL CROSS SECTIONS

Inclusive cross sections of particle production are reconstructed using an iterative procedure that includes particle yields and acceptance tables. The acceptance tables are preliminarily calculated for each setup configuration: recoil angle α, momentum P, and beam position. The measured particle yields depend on the beam position and shape; they decrease by several orders of magnitude when the settings change from the minimum momentum P ≈ 1 GeV/c to the maximum values. Therefore, the required procedure for calculating the cross section must take into account the momentum distributions inside the momentum acceptance for each setup configuration.

For thin targets (C, Al, Cu, W), the yield of the type i particle is

$${{Y}_{i}} = \frac{{\left( {\frac{{N(p)}}{{{{N}_{p}}}} - {{Y}_{{\text{BGR}}}}} \right)fr(i)}}{{{{N}_{{\text{TARG}}}}}}.$$
(2)

Here, N(p) is the number of all particles measured by the setup for the momentum P over time when Np protons were spilled on the target; YBGR is the normalized background, which was defined earlier by the Eq. (1); fr(i) is the fraction of particles of type i (i means π, K, p, etc.), which was determined using the time-of-flight system for a fixed momentum and a specific target.

For the hydrogen target, the expression for determining particle yields is different:

$${{Y}_{i}} = \frac{{f{{r}_{{\text{FULL}}}}(i)\left( {\frac{{N(P)}}{{{{N}_{p}}}} - \frac{{{\text{|}}\text{BGR}{\text{|}}}}{{{{N}_{{2p}}}}}} \right) - ~f{{r}_{{\text{EMPTY}}}}(i)\left( {\frac{{{\text{|}}\text{EMPTY}{\text{|}}}}{{{{N}_{{1p}}}}} - \frac{{{\text{|}}\text{BGR}{\kern 1pt} - {\kern 1pt} \text{EMPTY}{\text{|}}}}{{{{N}_{{3p}}}}}} \right)}}{{{{N}_{{\text{TARG}}}}}},$$
(3)

where |BGR|, |EMPTY|, and |BGR−EMPTY| are background measurements with the full target and the closed shutter, the empty target and the open shutter, and with the empty target and the closed shutter, respectively; frFULL and frEMPTY denote the fraction of the type i particles determined using the time-of-flight system for the full and empty targets, respectively. The difference in the data processing procedure for the liquid-hydrogen target is associated with the noticeable contribution of the background enriched with heavy nuclear fragments from the target flanges.

The additional normalization to the number of target atoms is defined as

$${{N}_{{\text{TARG}}}} = \frac{{{{N}_{{\text{A}}}}\rho t}}{A},$$
(4)

where A is the number of nucleons in a nucleus, NA is the Avogadro number, ρ is the target density, and t is the target thickness.

The acceptance tables εi(p, θ, φ, r) were calculated using the Geant4 simulation program for physical setups. The tables contain the probability that a particle of type i will produce a trigger signal in the setup, depending on its momentum P and on the angle (θ, φ) and point r of its production inside the target. The parameters φ and r cannot be included in the cross section, so the calculations were performed using the tables

$${{\varepsilon }_{i}}(p,\theta ) = \int {\int {\varepsilon (p,\theta ,\varphi ,{\mathbf{r}}){{d}^{3}}rd\varphi } } .$$
(5)

For antiprotons, protons, tritons, and deutons, this means the probability of passing through the magnetic channel of the setup from the radiation point to the final detector. While passing through the magnetic channel, a charged π meson may decay to produce a charged muon. Our time-of-flight system cannot distinguish such a muon from the parent π meson. Therefore, the tables for π mesons contain the probability that the meson or its decaying muon will reach the end of the setup through the Cherenkov detector, the trigger counters, and the time-of-flight system. For K mesons to be identified, it is necessary that they pass through the Cherenkov detector without decay. The simulation shows that if a K meson decays in the space between MRPC1 and MRPC2, its charged decay products do not generate a signal in all trigger counters, and such events can be neglected. Nevertheless, when the acceptance tables were calculated, the probability was evaluated that a K meson would pass through the Cherenkov counter or further, and, if it decays past the Cherenkov counter, pions or charged leptons from its decay would generate a signal in the trigger counters and detectors of the time-of-flight system. The acceptance tables have the following cell sizes for the momentum and angle:

$$\Delta p \leqslant 0.02P,\quad \Delta \theta \leqslant 0.008,\quad ~~\Delta \varphi \leqslant 0.01.$$

For each cell, the statistics was simulated so that the accuracy in calculating the efficiency for this cell (the binomial distribution) was 10−3 or better. The boundaries of the tables were determined by sequentially increasing the number of cells around the central region until the triggering efficiency for any cell at the volume boundary became less than 10−3.

After determining the boundaries of the table (the phase volume), the cell sizes were sequentially reduced by two times until the variation of the integral efficiency in the table became less than ~10−2.

The number of tables for each particle type is equal to the number of measured configurations. If the dependence of the cross section on the momentum \(\frac{{{{d}^{3}}\sigma (i,p,\alpha )E}}{{{{d}^{3}}p}} \equiv {{\sigma }_{i}}(p)\) is known, it is possible to calculate the yield of particles in each configuration of the setup. Calculations are performed via the integral

$${{Y}_{i}} \simeq {{y}_{i}} = \int {\int {{{\sigma }_{i}}(p){{\varepsilon }_{i}}(p,\theta )d{\text{cos}}(\theta )\frac{{{{p}^{2}}dp}}{E}.} } $$
(6)

This yield must coincide within the uncertainty with the yield defined in Eqs. (2) or (3). The reconstructed and measured yields are compared using the deviation function

$${\kern 1pt} {{\chi }_{i}} = \mathop \sum \limits_{k = N}^{k = 1} {{\left( {1 - \frac{{{{Y}_{i}}({{P}_{k}})}}{{{{y}_{i}}({{P}_{k}})}}} \right)}^{2}}\frac{1}{{Err_{k}^{2}}},$$
(7)

where the sum is taken for all experimental points, and Errk is the relative accuracy in measuring the yield at a selected point.

The continuous cross section σi(p) is specified by the values at N configuration points \({{\xi }_{i}}({{P}_{k}})\), which are then connected by the cubic spline

$$~{{\sigma }_{i}}(p) = f({{\xi }_{i}}({{P}_{k}})),\quad 1 \leqslant k \leqslant N.$$

The iterative procedure for reconstructing cross sections selects N values of \({{\xi }_{i}}({{P}_{k}})\) to minimize the function (7). In the first approximation, these values are

$$\xi _{i}^{1}(P) = \frac{{{{Y}_{i}}(P)}}{{\int {\int {{{\varepsilon }_{i}}(p,\theta )d\cos (\theta )\frac{{{{p}^{2}}dp}}{E}} } }}.$$

Further iterations consist in performing two operations for each point k sequentially from 1 to N. The first operation selects the offset \(\delta \xi \) simultaneously for all \(\xi ({{P}_{k}}),k \geqslant j\) so that the function (7) is minimal. After a proper correction, the second operation is performed, which selects the offset for the other part of the points: \(\xi ({{P}_{k}}),k < j\) when the function (7) is minimized. At the end of the cycle, k iterations are repeated until the relative change (between iterations) at each point ξi(Pk) becomes less than 10−3. The absolute error of the cross section is

$${\text{Err}}(\sigma ({{P}_{k}})) = \sigma ({{P}_{k}})\sqrt {{\text{Err}}_{k}^{2} + {{{(1 - y({{P}_{k}}){\text{/}}Y({{P}_{k}}))}}^{2}}} .$$

11 CONCLUSIONS

The main elements of the experimental setup were described, and their characteristics were presented. The parameters of the beam transfer line make it possible to eject up to 1013 particles per U-70 cycle to the target of the setup. The SPIN narrow-aperture focusing spectrometer is a system of seven magnetic elements, including dipole magnets and quadrupole lenses. The arrangement of the magnetic elements on mobile platforms makes it possible to select the angle for detection of secondary particles at angles in the range of 25°−55° with the beam direction. The beam diagnostic system is based on the use of secondary emission chambers, which provide long-term stability of the response and allow operation in a wide range of beam intensities. The target station is equipped with a telemechanics system, with which it is possible to select a sample of the target substance. The tracking system consists of a set of drift and proportional chambers that measure particle momenta with an accuracy of approximately 0.5%. The particle-type identification system is based on the threshold Cherenkov counter and multigap resistive plate chambers for the time-of-flight technique and is capable of separating particles with momenta of up to 4 GeV/c.