Who would have thought that simulating games of chance could be considered a serious scientific pursuit, giving birth to a technique capable of solving complex problems in physics? The story of the Monte Carlo method begins in the underground labs of the Manhattan Project and continues with modern supercomputers running neutron transport calculations. For more than 60 years, the use of this method for advanced neutronics codes has been aiding mankind in our quest to harness fusion energy.

Neutrons are an inevitable part of fusion. They are born within fusion reactions in plasmas composed either solely of deuterium ions, or of a mixture of deuterium and tritium. Being chargeless, neutrons escape from the plasma chamber, hitting the walls and penetrating deep into the tokamak’s structure. Neutrons are able to change the nuclei of the atoms they interact with – the consequences are either vital to the envisioned fusion device’s electricity production or destructive. It is therefore crucial to be able to predict how many neutrons are born in the plasma and in what manner they interact with their surroundings. To uncover the collective impact of neutrons, scientists perform complex neutron transport computations using sophisticated computer codes. These codes rely on the Monte Carlo method, and enable us to simulate the individual behaviour of billions of neutrons by drawing upon large quantities of random numbers. What the last century deemed science fiction has become science fact thanks to the rapid increase in the world’s computational power.


The question of whether random events are able to lead to concrete conclusions was first answered in the eighteenth century by an influential French scientist, Count Buffon. He proved it was possible to determine the value of pi by tossing baguettes onto a lined tile floor. Thus, the probability that a baguette will land on a crack is proportional to the mathematical constant. Moreover, he showed that the pi estimate was more accurate with every additional baked delicacy thrown over his shoulder. It was not until the Manhattan Project, designed for the development of nuclear weapons, that the fundamentals of the Monte Carlo method were established by some of the brightest minds of that era. The method is named after a casino in Monaco, since it enables complex physics problems to be solved by repeated random sampling, a process akin to playing games of chance.


The Monte Carlo method was applied to neutron physics from the very start, more specifically to the study of neutron travel through radiation shielding material. Although the theory of neutron transport has been well established using the Boltzmann equation, it proves difficult to solve analytically without significant simplifications. This is especially true for complex systems such as a tokamak. In contrast, modern Monte Carlo simulations treat deterministic problems by first finding a probabilistic analogue. This means the lives of neutrons in a fusion device, known as histories, are individually simulated from birth to absorption or loss from the system. The specifics of a neutron’s path – place of birth, direction of movement, distance travelled and type of interactions – are determined by random sampling of well-known physics phenomena. One can imagine the sampling process to be akin to throwingdice, the outcome of which defines the result of an event the neutron encounters. For example, if a neutron is bound to interact with an atom in the walls of the tokamak, we can use the knowledge of the probability of absorption, scattering or an inelastic scattering reaction and determine which one of the three will occur in the simulation – all based on the result of the roll of a dice.


The number of neutrons generated in a tokamak plasma is enormous. To get to an accurate representation of reality, several billions of neutron histories need to be simulated using Monte Carlo neutronics codes. In order to combine this with complex tokamak geometry, we need to perform a huge number of “dice rolls”, a task that is made possible by the increase in computational esources. The conclusions drawn from a multitude of single neutron simulations are analysed to obtain knowledge of quantities of interest. For example, the amount of tritium breeding, wall heating, material embrittlement or dose rates. It is somewhat counterintuitive to imagine that throwing dice might give us insight into not only what is going on in a fusion reactor, but also how galaxies have evolved or whether it is going to rain tomorrow. However, Monte Carlo simulations repeatedly prove to be a powerful tool in providing answers to problems that are difficult to solve analytically.

authorbox_Ziga-StancarSince I was a child I was captivated by the world of science, motivated by things we cannot yet explain. Working in neutronics, I am still mesmerised by the fact that one can successfully recreate the phenomena observed in large fusion devices by simulating an immense number of individual sub-atomic particles. I consider it a great honour to contribute my part to the mosaic of fusion energy research by way of my endeavours in neutron and plasma physics.

Žiga Štancar (27) from Slovenia is currently based at: Jožef Stefan Institute, Slovenia. (Picture: private)