Control fusion plasma | microwave | live formula | algebra | function plot
We have to use the cylindrical coordinates when the problem is cylindrical symmetry. For example, the eigenmode in a circular waveguide. Althrough there is a general theory for the differential operators in general curvilinear coordinates, it it very difficult to be understanded. There is also the formular for the differential operators in cylindrical coordinates. However … Read more
The electrons beam is usually confined by magnetics in the vacuum tube. The plasma is usually confined by magnetics in tokomaks. The motion is govend by the Newton’s 2nd law. However the cylinderical coordinates are used in both cases as the fields are axially symmetric. The common question is how to get the equations of … Read more
The AD650 is a charge balance voltage-to-frequency converter. The input signal is converted into an equivalent current by the input resistance RIN. This current is exactly balanced by an internal feedback current delivered in short, timed bursts from the switched 1 mA internal current source as shown in Fig.1. These bursts of current may be … Read more
The charges at the cathode reduces the potential that is present in the absence of the electron so that further emission is prevented. The maxium current is said to be the space charge limitation. Child and Langmuir first studied the space charge limitation in 1910s[1,2]. It assumes that two infinite parallel plane electrodes at fixed … Read more
Maxwell’s equation in vacuum Name Integral equations Differential equations Gauss’s law Gauss’s law for magnetism Maxwell–Faraday equation(Faraday’s law of induction) Ampère’s circuital law (with Maxwell’s addition) Next, We obtain the electromagnetic wave equation in a vacuum. It is also called Helmholtz equation. Take the Curl of the Faraday equation \(\nabla \times \left(\nabla \times \mathbf {E} \right)=\nabla \times … Read more
An electrton beam is widely used in all kinds of vacuum tubes. The electrons decrease the potential in and around the beam. The electrical force courses the beam to expand in the cavity. The main step to obtain the potential is as follows:Step 1 Use Gauss’s low to find the electric field in the cavity.Step … Read more
Asciimath is a markup language used to write mathematical expressions using plain text. It’s often used in online forums, blogs, and websites where users want to display math equations without using complex mathematical notation. ASCII Math provides a simple and intuitive way to represent mathematical symbols and expressions using standard keyboard characters. Operation symbols Type … Read more
Contour plot of the transverse electric mode in a circular cross section wave-guides. Plot real functions for one variable. Plasma tool permittivity Edit tool Latex replace tool Javascript Tool Javascript: export the formular from a form