## Sampling from Phase Space Distributions in 3D Charged Particle Beams

##### Christopher Boucher | September 22, 2016

In the previous installment of this series, we explained two concepts needed to model the release and propagation of real-world charged particle beams. We first introduced probability distribution functions in a purely mathematical sense and then discussed a specific type of distribution — the transverse phase space distribution of a charged particle beam in 2D. Now, let’s combine what we’ve learned and find out how to sample the initial positions and velocities of 3D beam particles from this distribution.

Read More##### Yosuke Mizuyama | September 21, 2016

The Gaussian beam is recognized as one of the most useful light sources. To describe the Gaussian beam, there is a mathematical formula called the paraxial Gaussian beam formula. Today, we’ll learn about this formula, including its limitations, by using the Electromagnetic Waves, Frequency Domain interface in the COMSOL Multiphysics® software. We’ll also provide further detail into a potential cause of error when utilizing this formula. In a later blog post, we’ll provide solutions to the limitations discussed here.

Read More##### Amelia Halliday | September 20, 2016

To optimize your modeling processes, there are a number of built-in materials available for you to use in the COMSOL Multiphysics® software. Along with these materials are features and functionality that allow you to efficiently assign materials to geometric entities in your model. These tools help expedite the process of assigning materials, specifying material properties, and even comparing the impact of different materials on your simulation results. Here, we’ll highlight three tutorial videos that showcase how to use such tools.

Read More##### Christopher Boucher | September 19, 2016

Previously in our Phase Space Distributions in Beam Physics series, we introduced probability distribution functions (PDFs) and various ways to sample from them in the COMSOL Multiphysics® software. Such knowledge of PDFs is necessary to understand how ion and electron beams propagate within real-world systems. In this installment, we’ll discuss the concepts of phase space and emittance as they apply to the release of ions or electrons in beams.

Read More##### Christopher Boucher | September 15, 2016

In this blog series, we’ll investigate the simulation of beams of ions or electrons using particle tracking techniques. We’ll begin by providing some background information on probability distribution functions and the different ways in which you can sample random numbers from them in the COMSOL Multiphysics® software. In later installments, we’ll show how this underlying mathematics can be used to accurately simulate the propagation of ion and electron beams in real-world systems.

Read More##### Hanna Gothäll | September 14, 2016

When addressing your geometry- and mesh-related support questions, we’ve noticed an increased use of STL files originating from 3D scan sources and meshes in NASTRAN® file format as bases for geometries. Performing simulations on these realistic objects can be challenging, particularly when preparing the geometry. Dealing with these files is now easier thanks to updates in the COMSOL Multiphysics® software. Learn how to utilize this functionality as well as how to achieve good results when importing STL and NASTRAN® files.

Read More##### Ionut Prodan | September 13, 2016

Today, guest blogger and Certified Consultant Ionut Prodan of Boffin Solutions, LLC discusses using a hybrid approach to calculate fracture flux in thin structures. When modeling thin fractures within a 3D porous matrix, you can efficiently describe their pressure field by modeling them as 2D objects via the Fracture Flow interface. Significant fracture flux calculation issues, however, may arise for systems of practical interest, such as hydraulic fractures contained within unconventional reservoirs. See how a hybrid approach overcomes such difficulties.

Read More##### Abbie Weingaertner | September 12, 2016

Polarizing beam splitters are optical devices used to split a single light beam into two beams of varying linear polarizations. These devices are useful for splitting high-intensity light beams like lasers as, unlike absorptive polarizers, they do not absorb or dissipate the energy of the rejected polarization state. See why creating a numerical modeling app offers a more efficient approach to analyzing and optimizing the design of these devices.

Read More##### Ed Fontes | September 9, 2016

In recent versions of the COMSOL Multiphysics® software, we’ve added several new multiphysics interfaces that include the constituent interfaces as separate physics interfaces, with the couplings predefined in the model tree’s Multiphysics node. This provides you with the best of both worlds, combining the flexibility of the constituent physics interfaces and the user-friendly nature of the predefined multiphysics couplings. The latest version of COMSOL Multiphysics® — version 5.2a — is no exception with the new Reacting Flow multiphysics interface.

Read More##### Caty Fairclough | September 8, 2016

Rotating machinery is an important element in many structures, from wind turbines to engines. The analysis of this rotating machinery — a field known as rotordynamics — is key in reducing noise and vibrations in many areas of technology. Here, we’ll take a closer look at rotordynamics and its relevance within various applications.

Read More##### Bridget Cunningham | September 7, 2016

Many modern devices leverage piezoelectricity. When analyzing the design of such devices, you want to be confident in the reliability of the obtained results. By utilizing the COMSOL Multiphysics® simulation software, you can achieve accurate results quickly. To prove it to you, we have created a benchmark model of a piezoelectric transducer.

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