Controlling the process of muon formation for muon-catalyzed fusion: method of non-destructive average muon sign detection

The recent development of intense muon sources (Holmlid, Swedish Patent SE 539,684 C 2 (2017)) is crucial for the use of muon-catalyzed fusion reactors (L. Holmlid, Fusion Science and Technology 75, 208 (2019)) which are likely to be the first generation of practical fusion reactors. For this purpose, only negative muons are useful. For existing sources where negative muons can be ejected (if not formed) preferentially, it is necessary to know the amount of negative muons to determine and optimize the fusion reactor efficiency on-line. Here, a method is developed to measure the absolute muon flux and its average sign without collecting or deflecting the muons. The muons from the patented muon generator have an energy of 100 MeV and above and an intensity of 1013 muons per laser pulse. Here, the detection of the relativistic laser-induced muons from H(0) is reported with a standard particle beam method, using a wire coil on a ferrite toroid as detector for the relativistic particles. The coil detection method shows that these relativistic particles are charged, thus not photons, neutrinos or neutral kaons. This makes the coil method superior to scintillator methods and it is the only possible method due to the large muon intensity. If an equal number of positive and negative mouns passed the coil, no signal would be observed. The signal at the coil in the case shown here is due to relativistic positive muons as concluded from a signal charge sign verification in the coil.

Effective Solid Angle Model and Monte Carlo Method: Improved Estimations to Measure Cosmic Muon Intensity at Sea Level in All Zenith Angles

Cosmic muons are highly energetic and penetrative particles and these figures are used for imaging of large and dense objects such as spent nuclear fuels in casks and special nuclear materials in cargo. Cosmic muon intensity depends on the incident angle (zenith angle, φ), and it is known that I(φ) = I0 cos2 φ at sea level. Low intensity of cosmic muon requires long measurement time to acquire statistically meaningful counts. Therefore, high-energy particle simulations e.g., GEANT4, are often used to guide measurement studies. However, the measurable cosmic muon count rate changes upon detector geometry and configuration. Here we develop an “effective solid angle” model to estimate experimental results more accurately than the simple cosine-squared model. We show that the cosine-squared model has large error at high zenith angles (φ ≥ 60°), whereas our model provides improved estimations at all zenith angles. We anticipate our model will enhance the ability to estimate actual measurable cosmic muon count rates in muon imaging applications by reducing the gap between simulation and measurement results. This will increase the value of modeling results and improve the quality of experiments and applications in muon detection and imaging.

MUON INTENSITY VARIATIONS AND ATMOSPHERIC TEMPERATURE

Muons in the atmosphere are formed during the decay of pions resulting from nuclear interactions of cosmic rays with nuclei of air atoms. The resulting muons are also unstable particles with a short lifetime. Therefore, not all of them reach the level of observation in the atmosphere. When the atmospheric temperature changes, the distance to the observation level changes too, thus leading to variations in the intensity of muons of temperature origin. These variations, caused by atmospheric temperature variations, are superimposed on continuous observations of muon telescopes. Their exclusion is, therefore, extremely necessary, especially in the data from modern muon telescopes whose statistical accuracy is very high. The contribution of various atmospheric layers to the total temperature effect is not the same for muons. This contribution is characterized by the distribution of the density of temperature coefficients for muons in the atmosphere. Using this distribution and the continuous intensity observations from the muon telescope in Novosibirsk, the inverse problem has been solved, from the solution of which the atmospheric temperature variations over a long period from 2004 to 2011 have been found. The results obtained are compared with aerological sounding data.

MUON INTENSITY VARIATIONS AND ATMOSPHERIC TEMPERATURE

Muons in the atmosphere are formed during the decay of pions resulting from nuclear interactions of cosmic rays with nuclei of air atoms. The resulting muons are also unstable particles with a short lifetime. Therefore, not all of them reach the level of observation in the atmosphere. When the atmospheric temperature changes, the distance to the observation level changes too, thus leading to variations in the intensity of muons of temperature origin. These variations, caused by atmospheric temperature variations, are superimposed on continuous observations of muon telescopes. Their exclusion is, therefore, extremely necessary, especially in the data from modern muon telescopes whose statistical accuracy is very high. The contribution of various atmospheric layers to the total temperature effect is not the same for muons. This contribution is characterized by the distribution of the density of temperature coefficients for muons in the atmosphere. Using this distribution and the continuous intensity observations from the muon telescope in Novosibirsk, the inverse problem has been solved, from the solution of which the atmospheric temperature variations over a long period from 2004 to 2011 have been found. The results obtained are compared with aerological sounding data.

Atmospheric effects of the cosmic-ray mu-meson component

Variations in the intensity of cosmic rays observed in the depth of the atmosphere include the atmospheric component of the variations. Cosmic-ray muon telescopes, along with the barometric effect, have a significant temperature effect due to the instability of detected particles. To take into account atmospheric effects in muon telescope data, meteorological coefficients of muon intensity are found. The meteorological coefficients of the intensity of muons recorded in the depth of the atmosphere are estimated from experimental data, using various methods of factor analysis. The results obtained from experimental data are compared with the results of theoretical calculations.

Atmospheric effects of the cosmic-ray mu-meson component

Variations in the intensity of cosmic rays observed in the depth of the atmosphere include the atmospheric component of the variations. Cosmic-ray muon telescopes, along with the barometric effect, have a significant temperature effect due to the instability of detected particles. To take into account atmospheric effects in muon telescope data, meteorological coeffi-cients of muon intensity are found. The meteorological coefficients of the intensity of muons recorded in the depth of the atmosphere are estimated from experi-mental data, using various methods of factor analysis. The results obtained from experimental data are com-pared with the results of theoretical calculations.

Distribution of temperature coefficient density for muons in the atmosphere

To date, several dozens of new muon detectors have been built. When studying cosmic-ray intensity variations with these detectors, located deep in the atmosphere, it is necessary to calculate all character-istics, including the distribution of temperature coeffi-cient density for muons in the atmosphere, taking into account their specific geometry. For this purpose, we calculate the density of temperature coefficients of muon intensity in the atmosphere at various zenith angles of detection at sea level and at various depths underground for different absorption ranges of primary protons and pions in the atmosphere.

Distribution of temperature coefficient density for muons in the atmosphere

To date, several dozens of new muon detectors have been built. When studying variations in cosmic-ray intensity with these detectors, located deep in the atmosphere, it is necessary to calculate all characteristics, including the distribution of temperature coefficient density for muons in the atmosphere, taking into account their specific geometry. For this purpose, we calculate the density of temperature coefficients of muon intensity in the atmosphere at various zenith angles of detection at sea level and at various depths underground for different absorption ranges of primary protons and pions in the atmosphere.