Technique for determining the kinetic energy of a hadron beam

Technique for determining the kinetic energy of a hadron beam using elements of the particle time of flight method, executed in a particle detector unit system equipped with a processing unit enabling the analysis of images recorded by the particle detectors and including an oscilloscope card with a minimum bandwidth of 200 MHz and a sampling frequency of at least 4 GS/s, characterised in that

• simultaneous, continuous recording of amplitude values for the SA and SB signals from the particle detector unit is started, with the first (A) and the second (B) detectors placed along the line of the studied hadron beam, with simultaneous parameters and specifications, located at a precisely determined mutual distance L and independently connected with the processing unit and comprising a previously calibrated system for execution of recording of the values of individual signal amplitudes SA and SB, which is executed with time resolution on the level of at least 0.5 ns,
• all amplitudes of the measured signals SA(k) and SB(k) from both detectors (A) and (B) are recorded simultaneously for a period of time corresponding to at least 100 times the theoretical time of flight of a single particle of the hadron beam between the detectors (A) and (B),
• the simultaneous records of amplitudes of the measured SA and SB signals from both particle detectors (A) and (B) are archived, and individual sampling points for both signals are recorded synchronously and indexed using the same variable specifying the recording step k, obtaining signal profiles SA(k) and SB(k),
• the amplitude value for signals SA(k) and SB(k) lower than the specified threshold value are considered to be zero and are eliminated,
• an analysis of the shape of individual signals SA(k) and SB(k) most frequently recorded for the protons of the measured beam is carried out and the shape pattern is determined for these signals, followed by the removal of signals deviating from this pattern,
• after the end of the recording period for amplitudes of signals SA(k) and SB(k) from both particle detectors (A) and (B), an analysis of the statistical correlation for the signal profiles for SA(k) and SB(k), left at both detectors by multiple particles, is carried out by shifting the recorded signal profile recorded from the particle detector (B) with its recording basis step k, compared to the constant signal profile from the particle detector (A), until the maximum overlap of signal profiles is achieved for SA(k) and SB(k), which is equivalent to achieving the minimum total difference between the amplitudes of signal profiles for SA(k) and SB(k), at the specified step k, corresponding to the time resolution used to record the signals,
• the number of steps k, determined during a measurement, from k=0 to k=N, is used to determine the multiplicity of steps k designated as τD, by which the signal SB(k) is shifted compared to the signal SA(k), such that the following function reaches its minimum:
• R
• ⁡
• (
• τ
• D
• )
• =
• 1
• N
• -
• τ
• D
• ⁢
• ∑
• k
• =
• 0
• N
• -
• τ
• D
• ❘
• "\[LeftBracketingBar]"
• S
• A
• (
• k
• )
• -
• S
• B
• (
• k
• +
• τ
• D
• )
• ❘
• "\[RightBracketingBar]"
• where:
• τD is a variable defining the shift between the compared signals and it assumes discreet values in the (0, N) range,
• the location of the global minimum of the R(τD) function and the value τDmin, corresponding to the time of flight of hadrons between the detectors (A) and (B) expressed using the formula t=Δt*τDmin, where Δt is the length of a single sample interval (0.5 ns), are determined,
• the position of the global minimum of the continuous R(τD) function is specified more precisely by fitting the polynomial around the previously determined minimum, using the least squares method for the distance (|R(τD)−ρ(τD)|), where ρ designates the fitted polynomial,
• the average time of flight of the hadron beam is determined according to the relationship, t=Δt*τmin, where Δt is the length of a single sampling interval, while τmin designates the real number τ, for which the ρ(τD) polynomial fitted to the R(τD) function reaches the minimum value,
• the kinetic energy value for the hadron beam is determined using the obtained time of flight t between the detectors A and (B) according to the known physical relationships for the given hadron beam,
• the determined value of kinetic energy of the hadron beam is corrected with the known energy loss occurring during the passage through the first detector (A), by subtracting the literature value of energy losses in the used detector (A),
• the procedure of kinetic energy determination for a hadron beam ends by presenting the determined energy value and with the removal of the (A) and (B) detectors from the motion path of the studied hadron beam.