Plasma Wakefield Acceleration

Wakefield particle acceleration is an exciting application of plasma physics which promises acceleration 10-1000 times greater than that of a traditional radio frequency cavity! Understanding it is key to creating more economical, compact, and higher energy particle accelerators for physics research in the future. The idea is to shoot a beam of ions through a plasma called a drive beam which creates electric wakefields. We can then place a witness beam behind the drive beam to be accelerated by those wakefields, transferring energy from the drive beam to the witness beam. In this article, we explore this process in 1D and 2D using techniques from plasma physics and discover interesting trends in the creation. All code can be found in the Github repo linked here.

1D Toy Model

When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$ For initial exploration of the plasma, we first formulate a 1D model which will effectively capture the qualitative behavior of plasma wakefield acceleration. We can do this with the following assumptions as they maintain the final derived plasma frequency in our analytic equations:

- The plasma is 1D \(\nabla \Rightarrow \frac{\partial}{\partial x})
- The plasma is a cold fluid \(p = 0)
- The plasma has immobile ions \(n_i = n_0 constant, v_i = 0)
- The plasma is electrostatic \(E = -\frac{d\phi}{dx})
- The plasma is affected by no magnetic fields \(B = 0)
- The plasma is non-relativistic
- The plasma is quasistatic (explained in depth later in the report)
- The plasma has a linear response to perturbations \($n = n_0 + n_1$, $v = v_0 + v_1$, $E = E_0 + E_1$)

My life story

I grew up in suburban Minnesota in the Rosemount-Apple Valley-Eagan area. Life before COVID-19 is uninteresting, I just watched YouTube and kids shows all day. If you talk to me in real life though, you know I love referencing things from this time like Naruto and Pewdiepie. When everyone went on lockdown, I became an annoying /mu/core kid who would just sit in his bed and listen to albums from front to back. I mean like really annoying, I got banned from the YouTuber deep cuts' Discord server. To be continued.

This is a separator line / divider:

---

Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.

Heading 4

Here are two columns:

Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr.

At vero eos et accusam et justo duo dolores et ea rebum.

Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr.

At vero eos et accusam et justo duo dolores et ea rebum.

Heading 5

This is an image:

This is a full-width image:

These are multiple images in a row:

Heading 6

Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat.