Magnetohydrodynamics SRJC Phys 43 Danny Delsuc Travis Wyatt

Magnetohydrodynamics SRJC, Phys 43 Danny Delsuc Travis Wyatt Y. Ataiiyan Spring 2011 Matt Moore Bryan Cote

Magneto – Hydro – Dynamics Magnetic Field– Liquid - Motion Agenda: • Intro to Magnetohydrodynamics (MHD). • Why this field is important. • History behind the creation of this field. • Mathematical analysis of its core concepts. • Overview of plasma and its part. • Current applications and devices. • Future Applications.

Magnetohydrodynamic Essentials • Magnetic Field • Perpendicular Current • Magnetic Fluid • Magnetic metals • Plasmas • Salt water • The idea of MHD is that magnetic fields can induce currents in a moving conductive fluid, which create forces on the fluid. The set of equations which describe MHD are a combination of the Navier. Stokes equations of fluid dynamics and Maxwell's equations of electromagnetism.

Why MHD is Important • The ability to create a force between two different mediums, without contact. • An engine that does not need a rotor or turbine to create motion, therefore nearly eliminating engine degradation caused from moving parts. • The resistivity caused by its various mediums is comparably low when analyzed along side current engines, due to MHD’s utilization of fluids and gases. • Various applications across a multitude of fields, which will be presented in detail shortly.

The Beginning of MHD • 1812: Michael Faraday creates the first homopolar motor. • The motor ran by running an electric current through a wire that hangs next to a magnet. • This setup generates an electromagnetic force that drives the wire in circles. • To get current through the wire, you need a connection at both ends, so Faraday used mercury, which allows the loose end to move freely.

How They Figured This Out Dr. William Hyde Wollaston • In 1851, Dr. William Hyde Wollaston was able to measure the voltage induced by the tide in the English Channel. • Michael Faraday had previously attempted a similar experiment in 1832 by trying to measure the current produced by water flowing past the Waterloo Bridge as it interacts with the Earth's magnetic field but the equipment of the time was unable to read to small current. • Instead of seeing how a magnetic field and current affected salt water, he analyzed how saltwater and magnetic field induce a current.

How They Figured This Out • • Hannes Alven 1942: First recorded to use the word magnetohydrodynamics. Magnetohydrodynamics was used in reference to the transfer of momentum from the Sun to the planets, but is eventually exanded upon to include the current field. Received 1970 Nobel Prize in Physics for his work on magnetohydrodynamics. Described a classification of waves now known as Alfvén waves. These waves analyze the low travelling oscillations of a plasma in a magnetic field. The wave eventually changes into the magnetosonic wave when the propagation is perpendicular to the magnetic field. The wave is dispersionless.

Conceptually What’s Going On A B Key • Blue Line: Magnetic Field • Purple Line: Current • Green Line: Motion • In the figure A, we have a current that runs down the screw and into he magnetic, traveling at a 90 o andle through the magnet and out the wire; this current and magnetic field causes a force that’s orthogonal to both forces, causing the magnet to spin while it is magnetically attached to the screw. • The same thing happens in figure B, however, instead of the force being exerted on the magnet, the salt water that the magnet is submerged in rotates instead due to the resulting Lorentz force which is applied to the water and not the magnet.

Mathematically What’s Going On Series of Fundamental Equations: • Maxwell’s Equation of Electromagnetism • Navier-Stokes Equations of Fluid Dynamics These differential equations can be solved simultaneously, either analytically or numerically.

Mathematically What’s Going On Maxwell’s Equations (Almost a collection of other equations…) ‘Microscopic’ Equations ‘Macroscopic’ Equations

Navier-Stokes Equations

Confused? ? ?

You’re Not The Only One…

What We’ve Simplified It To: Right Hand Rule Applies!

A Hidden Component: Plasma • Plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. • Plasmas contain charged particles: positive ions and negative electrons. • The presence of a non-negligible number of charge carriers makes the plasma electrically conductive so that it responds strongly to electromagnetic fields. • Due to its attributes, plasma is sometimes considered the fourth state of matter. • Despite plasma having similar properties as a gas, it may form structures such as filaments, beams and double layers when in the presence of a magnetic field. • Although rarely found on Earth, plasmas make up over 99% of the universe

Plasma and its Part • Similar to liquid metal and salt water, plasmas conduct electricity and are magnetic. • Since MHD requires a medium that exhibits these attributes, plasma is a viable medium. • The picture to the left illustrates the motion of a plasma moving along a magnetic field. • Magnetic field lines cannot move through the plasma without generating electric forces that resist the motion-making plasma and MHD extremely compatible.

Brief Plasma Theory • All plasma is not created equal. • Since plasma needs to be first ionized in order to be created, it is subject to variation due to the ionization process. • To compensate for this variation, the term "plasma density" by itself usually refers to the "electron density", that is, the number of free electrons per unit volume. • The degree of ionization of a plasma is the proportion of atoms that have lost (or gained) electrons, and is controlled mostly by the temperature. • The degree of ionization, α is defined as α = ni/(ni + na) where ni is the number density of ions and na is the number density of neutral atoms. • Due to the complexity by which plasmas are analyzed, their behavior is can be seen through two different models: • Fluid Model: One simple fluid model, magnetohydrodynamics, treats the plasma as a single fluid governed by a combination of Maxwell's equations and the Navier– Stokes equations. • Kinetic Model: is based on representing the smoothed distribution function on a grid in velocity and position. The other, known as the particle-in-cell (PIC) technique, follows the trajectories of a large number of individual particles. Kinetic models are generally more computationally intensive than fluid models.

Current Applications: Engineering Tokamak Magnetic Confinement International Thermonuclear Experimental Reactor: France • Fusion reactions combine light atomic nuclei such as hydrogen to form heavier ones such as helium. • To overcome the electrostatic repulsion between them, the neutral atoms are heated by tens of millions of degrees until they exist in a plasma state. • Magnetic confinement fusion attempts to create the conditions needed for fusion energy production by using the electrical conductivity of the plasma to contain it with magnetic fields. • This can be thought of as a balance between magnetic pressure and plasma pressure, or in terms of individual particles spiraling along magnetic field lines.

Current Applications: Medicine • Currently being developed for cancer treatment. • Treatment begins by injecting a patient intravenously with a drug that’s either encapsulated into a magnetic microsphere (or nanosphere) or conjugated on the surface of the micro/nanosphere. • A megnetic field is then applied to the target site of the patient, thus allowing them to deliver the drug locally. • Very high concentration of chemotherapeutic agents can be achieved near the target site without any toxic effect to normal surrounding tissue or to whole body.

Current Applications: Geophysics • MHD is used to predict the inverting of the Earth’s magnetic poles. • Based on the MHD equations, Glatzmaier and Paul Roberts have made a supercomputer model of the Earth's interior. • Beneath the Earth's mantle, lies the core which is made up of two parts - the solid inner core and liquid outer core - both have significant quantities of iron. • The liquid outer core moves in the presence of the magnetic field and eddies. These eddies develop a magnetic field which boosts Earth's original magnetic field • This process which is self-sustaining, is called the geomagnetic dynamo.

Current Applications: Transportation • Built in the early 1990 s by "The Mitsubishi Group" , in place of a propeller or paddle wheel, the Yamato 1 uses jets of water produced by a magnetohydrodynamic propulsion system • Inside each thruster, the seawater flows into six identical tubes, arranged in a circle like a cluster of rocket engines. • The tubes are individually wrapped in saddle shaped superconducting magnetic coils made of niobium titanium alloy filaments packed into wires with copper cores and shells. • Liquid helium cools the coils to – 452. 13°F, just a few degrees above absolute zero, keeping them in a superconducting state in which they have almost no resistance to electricity. • Electricity flowing through the coils generates powerful magnetic fields within the thruster tubes. • When an electric current is passed between a pair of electrodes inside each tube, seawater is forcefully ejected from the tubes, jetting the craft forward.

Future Applications: Flight • University of Florida mechanical and aerospace engineering associate professor Subrata Roy has submitted a patent application for a circular, spinning aircraft design. • The vehicle will be powered by a magnetohydrodynamics • Electrodes will cover each of the vehicle’s surfaces and ionize the surrounding air into plasma. • The force created by passing an electrical current through this plasma pushes around the surrounding air, and that swirling air creates lift and momentum and provides stability against wind gusts.

References • • • • • • http: //www. kollewin. com/blog/magneto-hydro-dynamics/ http: //www. popsci. com/diy/article/2006 -08/playing-poison http: //www. evilmadscientist. com/article. php/Simple. MHD http: //www. scribd. com/doc/40534504/Magneto-Hydrodynamics http: //astronomy. swin. edu. au/study/PC_MHD. pdf http: //upload. wikimedia. org/wikipedia/commons/1/18/Tcv_int. jpg http: //img. medscape. com/article/712/338/712338 -fig 2. jpg http: //www. pharmainfo. net/reviews/magnetic-microcarriers-novel-approach-targeted-drugdelivery http: //farm 3. static. flickr. com/2156/1895129843_a 38 c 38 e 1 bd. jpg http: //www. skewsme. com/mhd. html http: //library. thinkquest. org/08 aug/01930/graphics/pagegraphics/mercury_pouring. jpg http: //facstaff. unca. edu/chennon/images/ocean. jpg http: //www. thunderbolts. info/forum/php. BB 3/viewtopic. php? p=8010 http: //www. esacademic. com/pictures/eswiki/77/Michael-faraday 3. jpg http: //www. palladiumcoins. com/images/wollaston-256. jpg http: //en. wikipedia. org/wiki/File: Young. Alfven. jpg http: //www. mondolithic. com/? p=435 http: //www. rzg. mpg. de/visualisation/scientificdata/rzgprojects/mhd. jpg http: //www. elec-intro. com/EX/05 -14 -04/f 21019. jpg http: //euroross. blogspot. com/Confused%20 Bush. jpg http: //www. spiffynova. com/wp-content/uploads/2009/04/cat_with_rubix_cube. jpg http: //xenophilius. files. wordpress. com/2008/06/080611135049. jpg http: //www-solar. mcs. st-andrews. ac. uk/cluster/solar_flare. jpg http: //fc 04. deviantart. net/fs 48/f/2009/199/2/a/Plasma_by_Gerbit. jpg