AS 4002 Star Formation & Plasma Astrophysics BACKGROUND: Maxwell’s Equations (mks) H (the magnetic field) and D (the electric displacement) to eliminate.

Slides:

Advertisements

Similar presentations

Magnetic field II. Plan Motion of charge particle in electric and magnetic fields Some applications of magnetic fields.

Advertisements

Advanced Higher Physics Unit 2

Physics of fusion power

Basic Plasma Physics Principles Gordon Emslie Oklahoma State University.

MHD Concepts and Equations Handout – Walk-through.

Meanwhile, somewhere in California. Solar plasma Convection is complicated Temperature is very high Completely or partially ionized gas -> Charges (protons.

Space plasma physics Basic plasma properties and equations Space plasmas, examples and phenomenology Single particle motion and trapped particles Collisions.

Single particle motion and trapped particles

Plasma Astrophysics Chapter 3: Kinetic Theory Yosuke Mizuno Institute of Astronomy National Tsing-Hua University.

Physics of fusion power Lecture 6: Conserved quantities / Mirror device / tokamak.

2/xx/07184 Lecture 221 PHY 184 Week 6 Spring 2007 Lecture 22 Title: The Lorentz Force = q v x B.

Charged Particles in Electric and Magnetic Fields Motion of charged particles Lorentz Force Examples: cyclotron, mass spectrometer.

The formation of stars and planets Day 1, Topic 3: Hydrodynamics and Magneto-hydrodynamics Lecture by: C.P. Dullemond.

Fluid equations, magnetohydrodynamics Multi-fluid theory Equation of state Single-fluid theory Generalised Ohm‘s law Magnetic tension and plasma beta Stationarity.

Chapter 25 Electric Potential

Problem 2 Find the torque about the left hand segment on the loop as a function of θ, the angle the plane makes with the horizontal plane.

Physics 121: Electricity & Magnetism – Lecture 9 Magnetic Fields Dale E. Gary Wenda Cao NJIT Physics Department.

5. Simplified Transport Equations We want to derive two fundamental transport properties, diffusion and viscosity. Unable to handle the 13-moment system.

Viscosity. Average Speed The Maxwell-Boltzmann distribution is a function of the particle speed. The average speed follows from integration.  Spherical.

Lecture “Planet Formation” Topic: Introduction to hydrodynamics and magnetohydrodynamics Lecture by: C.P. Dullemond.

Chapter 28 Magnetic Fields Key contents Magnetic fields and the Lorentz force The Hall effect Magnetic force on current The magnetic dipole moment.

Physics of fusion power Lecture 7: particle motion.

Physics of Fusion power Lecture4 : Quasi-neutrality Force on the plasma.

Magnetic Fields AP Physics C Montwood High School R. Casao.

Chapter 7 Electrodynamics

MHS Physics Department AP Unit III D1. Magnetic Fields Students should understand the force experienced by a charged particle in a magnetic field, so.

Chapter 5 Diffusion and resistivity

General electric flux definition

Accelerating Charge Through A Potential Difference.

Space physics EF2245 Tomas Karlsson Space and Plasma Physics School of Electrical Engineering EF2245 Space Physics 2009.

AS 4002 Star Formation & Plasma Astrophysics Supercritical clouds Rapid contraction. Fragmentation into subregions –Also supercritical if size R ≥ clump.

Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics 20-nov-2008.

Light and Matter Tim Freegarde School of Physics & Astronomy University of Southampton Classical electrodynamics.

Boundaries, shocks, and discontinuities. How discontinuities form Often due to “wave steepening” Example in ordinary fluid: –V s 2 = dP/d  m –P/  

ASEN 5335 Aerospace Environments -- Radiation Belts1 The Radiation Belts A radiation belt is a population of energetic particles stably-trapped by the.

1 Magnetostatics The Basics. 2 Stationary charge: Stationary charge: v q = 0 E  0B = 0 Moving charge:Moving charge: v q  0 and v q = constant E  0B.

Electricity and Magnetism Explore the second of the four fundamental forces in nature –Gravity –Electricity and Magnetism –Weak Nuclear Force –Strong Force.

Sun is NOT a normal gas B and plasma -- coupled (intimate, subtle) behaves differently from normal gas: 2. MHD Equations Sun is in 4th state of matter.

Interactions between Electricity and Magnetism Interactions between electricity and magnetism all involve some motion of either charges (electricity) or.

Magnetic Force and Circular Motion Mrs. Coyle AP Physics C.

Day 2 Charged Particles Moving Through Magnetic Fields

Advanced EM - Master in Physics Poynting’s theorem Momentum conservation Just as we arrived to the Poynting theorem – which represents the.

Maxwell's Equations & Light Waves

CH Review -- how electric and magnetic fields are created Any charged particle creates an electric field at all points in space around it. A moving.

Space physics EF2245 Tomas Karlsson Space and Plasma Physics School of Electrical Engineering EF2245 Space Physics 2010.

Prof. David R. Jackson ECE Dept. Spring 2015 Notes 28 ECE 2317 Applied Electricity and Magnetism 1.

Maxwell’s equations in a medium

Chapter 25 Electric Potential. Like gravity, the electric force is conservative: it has a Potential Energy. A charge in an electric field has electric.

Introduction to Plasma Physics and Plasma-based Acceleration

Introduction to Plasma Physics and Plasma-based Acceleration

High Energy Observational Astrophysics. 1 Processes that emit X-rays and Gamma rays.

Electromagnetic Theory

Particle in uniform B-field

Magnetic Force on Moving Charged Particles.

ELEC 3105 Basic EM and Power Engineering

Charge in a constant uniform electric & magnetic field

Electric Field & Magnetic Field

Maxwell's Equations and Light Waves

Maxwell's Equations & Light Waves

Larmor Orbits The general solution of the harmonic oscillator equation

Chapter 3 Plasma as fluids

Physics 014 Magnetic Fields.

Charged Particles in Electric and Magnetic Fields

Earth’s Ionosphere Lecture 13

Lesson 3 Forces and Fields

Mechanical Energy Kinetic Energy, energy of motion,

Movement of Charges In a Magnetic Field.

Chapter 28 Magnetic Fields

LECTURE I: SINGLE-PARTICLE MOTIONS IN ELECTRIC AND MAGNETIC FIELDS

Equation relating speed, frequency, and wavelength of a wave

Presentation transcript:

AS 4002 Star Formation & Plasma Astrophysics BACKGROUND: Maxwell’s Equations (mks) H (the magnetic field) and D (the electric displacement) to eliminate Since We have used

AS 4002 Star Formation & Plasma Astrophysics The magnetic permeability Charge density Electric field Current density Observers often measure magnetic induction in Gauss (rather than Tesla) and energy in erg (rather than Joules) The permittivity of free space Definitions and Units

AS 4002 Star Formation & Plasma Astrophysics THE MAGNETOHYDRODYNAMIC (MHD) EQUATIONS: DERIVATION These equations describe how a magnetic field interacts with a plasma (ionized gas). What happens when you put a magnetic field into a plasma? Force (F) on a particle of charge (q) moving in an electric field (E) and a magnetic field (B):

AS 4002 Star Formation & Plasma Astrophysics Simple case No electric field E = 0 Uniform magnetic field B = (0,0,B) Force equation has components z x y B

AS 4002 Star Formation & Plasma Astrophysics Resultant particle motion The solution describes helical motion and the perpendicular velocity is constant where the gyro frequency (or Larmor frequency) B The gyroradius

AS 4002 Star Formation & Plasma Astrophysics Consequences Charged particles are tied to fieldlines (electrons and protons gyrate in opposite directions). Even when the plasma is effectively collisionless ( mean free path >> typical lengthscales ) the magnetic field causes the plasma to behave collectively. The gyroradius defines the lengthscale on which particle motions are organised.

AS 4002 Star Formation & Plasma Astrophysics Both conductivity and viscosity across magnetic field lines are much less than that along field lines. Applying a uniform electric field perpendicular to B causes the centre of the helix to drift in the direction of E, while applying an electric field along B causes particles to be accelerated.

AS 4002 Star Formation & Plasma Astrophysics The Equation of Motion The equation of motion for charged particles is where n is the particle number density, m is the particle mass, F is a combination of the Lorentz force and gravity, p is the pressure (assumed to be a scalar), and P describes the momentum transfer by collisions.

AS 4002 Star Formation & Plasma Astrophysics Write this equation separately for electrons and ions: Add these using

AS 4002 Star Formation & Plasma Astrophysics to get This is just the same as the normal equation of motion for a fluid, except for the Lorentz force which describes the interaction between the magnetic field and the plasma.