## 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##### 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##### Caty Fairclough | July 25, 2016

Quadrupole mass filters, the key component of quadrupole mass spectrometers, filter ions by their charge-to-mass ratio, only allowing ions with a certain ratio to pass through the device. As such, a high transmission probability for a specific ion through the filter is desirable. However, fringe fields in the mass filter can affect this probability. By using multiphysics simulation, we can take a closer look at quadrupole mass filters and investigate the effect of fringe fields on these devices.

Read More##### Christopher Boucher | June 8, 2016

Static mixers are well-established tools in a wide variety of engineering disciplines due to their efficiency, low cost, ease of installation, and minimal maintenance requirements. When evaluating whether a mixer can be used for a certain purpose, it is important to determine whether the resulting mixture is sufficiently uniform. In this blog post, we will discuss the setup of an app designed to quantitatively and qualitatively analyze the performance of a static mixer using the Particle Tracing Module.

Read More##### Bridget Cunningham | March 1, 2016

When diagnosed with end-stage renal disease (ESRD), a form of permanent kidney failure, patients must undergo dialysis to replace the blood cleaning function of kidneys. Dialysis requires vascular access, a process where blood is removed, purified, and returned to the patient’s vasculature. Current methods for providing access, however, suffer from high failure rates. Combining CFD simulations with shape optimization techniques provides a way to better understand and predict such failure.

Read More##### Walter Frei | December 29, 2015

While designing a structure, have you ever been unsure of how to achieve the best shape? If so, then you will want to add a useful technique called shape optimization to your COMSOL Multiphysics modeling skill set. Today, we will discuss the concept of shape optimization and demonstrate its use through a classical problem.

Read More##### Walter Frei | December 24, 2015

In this blog post, we will introduce the concept of shape optimization for adjusting part dimensions by using analytic sensitivity methods. If you have a single objective function that you want to improve, a set of geometric parameters that you want to change, as well as a set of constraints, then you can use the functionality of the Optimization Module and the Deformed Geometry interface in COMSOL Multiphysics to find the optimal structure without any remeshing. Let’s find out how!

Read More##### Aditi Karandikar | December 23, 2015

3D printing, also known as additive manufacturing, has been a popular topic of discussion on the COMSOL Blog and throughout the scientific community. New initiatives have furthered the capabilities of this technology, while extending its reach in various fields of research, manufacturing, and design. With the help of COMSOL Multiphysics, researchers at the Netherlands Organization for Applied Scientific Research (TNO) are investigating the promise of 3D printing in the realm of material design.

Read More##### Fanny Littmarck | December 2, 2015

Healthcare-associated infections (HAI) affect millions of people around the globe. While the most common cause of HAI is direct contact with the source, airborne bacteria may also play a role in patient infections. To prevent airborne infection and make hospital clean rooms safer, it’s important to design efficient ventilation systems. As an added benefit, efficient ventilation designs also lead to lower energy-related costs. The first step to a better design is CFD modeling.

Read More##### Daniel Smith | November 19, 2015

Many different tools are available for counting particles. Choosing the optimal method depends on the application; specifically, whether you want to use the number of counted particles in equations or during postprocessing. The Particle Tracing interfaces in COMSOL Multiphysics feature three main particle counting options. While these approaches are versatile enough to compute quantities such as charge density and momentum flux, our focus here will be computing the number of particles on a set of domains or boundaries.

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