C++ library for numerical FBBC-detector simulations (for NICA project).

To meet the challenges of the fast monitoring of the beam-beam collisions of the high-intensity NICA beams, the compact MCP-based Fast Beam-Beam Collisions (FBBC) detector with high timing properties was proposed in (A.A. Baldin, G.A. Feofilov, P. Har'yuzov, F.F. Valiev, NIMA, v.958, 1 (2020), 162154). The FBBC is based on the application of Microchannel plate detectors (Fig.1) for the precise determination of arrival times of charged particles produced in the nucleus-nucleus collisions at NICA.

We supposed FBBC as two sets of MCPs placed on the left and right sides symmetrically from the interaction point (Fig.2). The number of MCPs on the single side is optional. We suppose every single MCP is a ring with some inner and outer diameters. MCP is separated into some amount of sectors, one of them is connected to a read-out electronic channel (Fig.1).

• fbbc-lib.h which contains function prototypes and in which our FBBC-class members and ParticleFBBC structure are defined;
• fbbc-lib.cpp in which the methods of your analysis are implemented;

• double RZtoEta(double r, double z) - calculates pseudorapidity η using formulas θ=atan(r/z) and η=-log(tan(θ/2)), where (r,φ,z) is given particle coordinate (in cilindrical coordinates) relatively interaction point (0,0,0).
• double GetRandomNumber(const double first=0, const double last=1) - returns a random number, generated with uniform distribution in the interval [first, last]. If no arguments, given interval equals [0, 1].

In short, this structure defines the way that FBBC "see" particles. It is supposed, that every particle in a single collision can be fully described (from a point of view of the FBBC detector facility) with:

• index number Id,
• energy E,
• momentum P,
• its longitudinal component Pz,
• polar angle Phi,
• Z coordinate of the interaction point.

With knowledge of E, P, Pz, Phi, and Z we can calculate coordinates of particle contact with MCP plates and the time of this contact. Index number Id provides us an ability to go back from ParticleFBBC to the initial particle format (e.g. ROOT branch).

This structure contains the possible information about times of particles passed through the plate and registered by the detector, their Ids, and the number of MCP sector which registered the particle. Shortly speaking, PartTime is constructed with the next fields:

• Time of arrival of a particle on MCP Time,
• particle index number Id,
• number of radial sector Rad_sec, which particle passed through,
• number of angular sector Ang_sec, which particle passed through.

This information can be extracted later since method GetOutputVector() (see later) returns vectors of this structures.

This is the main library class, which simulates the work of the FBBC detector facility. At the input it accepts a vector of particles in ParticleFBBC format (vector). At the output is returns a vector of vectors of pairs <time, Id>, where Id is particle index number Id (see ParticleFBBC structure) and time is the time of particle contact with the i-th MCP plate of FBBC.

• vector plates_distances is the vector of distances of MCP plates from the detector center;

• size_t plates_number is the number of plates (size of plates_distances vector);

• double r_in is inner (small) radius of every MCP plate;

• double r_out is outer (big) radius of every MCP plate;

• size_t rad_sec_num is the number of radial sector separations;

• size_t ang_sec_num is the number of angular sector separations;

• double efficiency is the efficiency of every MCP plate (a probability to register particle which passed through MCP);

• double time_prec is the time precision of every sector of every MCP plate;

• vector particles is the vector of particles in considered event (converted to ParticleFBBC format);

• vector PassThrowMCP(const size_t mcp_num) is the method which "simulates" passage of particles through MCP with a number mcp_num and returns vector of PartTime-structures, which contains

• vector<vector> PassThrowDetector() return the vector of the results of PassThrowMCP method calcuations for every MCP plate.

• const size_t GetPlatesNumber() const returns plates_number;

• const double GetEfficiency() const returns efficiency;

• const double GetTimePrecision() const returns time_prec;

• const double GetRInner() const returns r_in;

• const double GetROuter() const returns r_out;

• const size_t GetRadialSecNumber() const returns rad_sec_num;

• const size_t GetAngularSecNumber() const returns ang_sec_num;

• const vector GetPlatesDistances() const returns plates_distances vector;

• const vector<vector> GetPlatesPseudorapidity() const converts plates_distances, r_in, r_out and Z coordinate of event into pseudorapidity interavals (using function RZtoEta) covered by every MCP plate;

• void SetParticlesFBBC(const vector parts) initializes "vector particles" from "parts" vector;

• vector<vector> GetOutputVector() returns the result of PassThrowDetector() evaluation.

For example the result of SMASH event generator(https://smash-transport.github.io/) 100 simulations of AuAu collisions at sqrt(s)=11GeV was used. To run the script one should type in the 'example_script' folder command (from a terminal): root example.cxx