Control fusion plasma | microwave | live formula | algebra | function plot
In the world of high-power microwave engineering, one of the most fundamental challenges is efficiently transmitting energy from a confined metal pipe out into open space. This is not just an academic exercise; it is a critical enabling technology for applications like radar, communications, and cutting-edge fusion energy research in systems like Electron Cyclotron Resonance … Read more
The derivation of the magnetic field of a dipole is a cornerstone of any course in electromagnetism. Traditionally, it’s a rite of passage involving pages of careful vector algebra, complex integrals, and approximations—a process as rewarding as it is prone to error. But what if we could map the fundamental physics directly into a calculation, … Read more
In scientific computing, especially in fields like optical physics and signal processing, we often work with iterative algorithms that are computationally intensive. Every microsecond saved in the core loop can translate into minutes or even hours saved on a full simulation. One such common operation, particularly in phase retrieval algorithms like Gerchberg-Saxton, is the need … Read more
JupyterLab is a powerful, browser-based interactive computing environment that blends code, text, and visualization in a single interface. Much like Mathematica, it allows users to write and execute code alongside narrative text, mathematical expressions, plots, and interactive widgets. But unlike Mathematica, JupyterLab is open-source, free to use, and part of the larger Project Jupyter ecosystem. … Read more
Camera projection is a fascinating and fundamental concept in all 3D graphics. Imagine you are a photographer in a large room. To take a picture, you do two main things: The matrices mathematically model these two steps. Our goal is to take a point in the 3D world (like a corner of our image) and … Read more
1. The Problem: The Invisible Power and Peril of Magnetic Fields From the life-saving images of Magnetic Resonance Imaging (MRI) to the colossal energies of the Large Hadron Collider, powerful electromagnets are cornerstone technologies of modern science and medicine. They operate on a simple principle—running an electrical current through a coil of wire to generate … Read more
Ever wondered how tiny charged particles like electrons behave when they encounter powerful electric and magnetic fields? Imagine being able to not just read about it, but to see it happen, to tweak the conditions, and to observe the intricate dance in real-time. Our new interactive web application, the Electron Cyclotron Motion Simulator, lets you … Read more
Tired of wrestling with complex polynomial equations and curious about their hidden structure or the nature of their roots? Step into a world of mathematical clarity with our brand new Web Polynomial Analyzer, your interactive gateway to exploring the fascinating realm of polynomials directly from your browser. We’ve designed this tool with no downloads or … Read more
1. Introduction: Modeling High-Power Electromagnetic Beams The precise generation, transmission, and manipulation of high-power microwave (HPM) and millimeter-wave (MMW) beams are critical for a range of advanced scientific and industrial applications. These include plasma heating in fusion energy research (like Electron Cyclotron Resonance Heating – ECRH), directed energy systems, high-resolution radar, industrial material processing, and … Read more
Our world is alive with waves – from the gentle ripples on a pond to the invisible carriers of sound and light. When these waves meet, they don’t simply pass by; they interact in a mesmerizing dance of reinforcement and cancellation, a phenomenon known as interference. This principle is fundamental, shaping how we perceive sound, … Read more