The forth state of matter.
Solids, fluids and gasses being the first three states of matter.
Matter is in the state of plasma when the element is ionized. A more classical definition would include the statement "the free electron or its replacement is within the vicinity of the ion." The reasoning being, there is no element if the electron or replacement is missing. If the electron or electrons are close to the element then a quasineutral element is created which is charged and neutral at the same time.
A gas, is the state of matter in a form as the air we breath. Ionization, is to take matter and "Electrically Stretch" it and not just a little tug, either! Arc welding and lightning are forms of plasma. Plasma is a state of matter not conducive to the human's standard of living requirements.
A plasma mass is a group of elements in a quasineutral gas of charged and neutrals particles which exhibit collective behavior. Examples of matter in the universe in the plasma state are; the solar wind, Sun, Corona, ionosphere, and fusion reaction. It is possible that more than 99 percent of the universe's matter is in the plasma state.
Plasma reacts to and affects: electric, magnetic, electromagnetic and gravitational laws. Plasma takes on many characteristics of the other states of matter like: acoustics, supersonics, dynamics and thermodynamics. Plasmatic and nonplasmatic material can coexist; the general rule is that this condition is usually fragile.
Electric lightning bolts and NE-2 relaxation oscillators both work the same. In clouds, power is supplied by static action and in the oscillator it is an electric power supply. As the voltage or charge builds up across the gaseous element (Air or NE-2) the ionization potential is reached and the gas ionizes, becoming plasmatic. As a plasma the gas conducts allowing current flow. Current flow creates higher heat and the gas becomes more plasmatic and a better conductor, thus, more current flows. In the NE-2 case, power depletes, can not maintain the thermal requirements for the plasma, and the gas stops being plasmatic. Again, air becomes a good insulator. Current stops and the supply rebuilds. Until, the ionization potential is again reached.
In the case of lightning, a general lightning bolt is made up of a group of strikes or discharges. The common statement known as "Lightning never strikes the same place twice." is a fallacy. Lightning hits the same a hundred times right off.
The ionization energy is the energy required to remove a given electron from its atomic orbit and place it at rest some place at an infinite distance from the ion. The energy function is dependent upon the type of element, the degree of ionization, and the current molecular consistency.
Plasma has both T-electron and T-ion temperatures with three degrees of freedom. Plasma follows the laws of conservation of energy, vectored forces and cause & effect. Plasma's magnetohydrodynamic power makes it capable of the dynamo. Plasma will act as an electric energy generator without the encumbrances of a heat cycle and act as an engine to do work. Plasma will also wave and form eddy currents which can be called perturbations. Based upon temperature, a substance will have certain amount of ionized atoms within a larger amount of atoms. At highly elevated temperatures the complete body will be ionized. At very low temperatures none of the atoms will be ionized. A general approximation for thermal equilibrium is the Saha equation:
The Saha equation tells us the amount of ionization to be expected in a gas in thermal equilibrium.
The explanation of plasma is not exact because of its hot nature. Plasma reacts to many different forces. This makes plasma difficult to describe mathematically. However, many problems are solved by taking the limits of action and associating the results with experimentation. Many experiments have been done with plasma. Just watching a lightning storm will give an indication of how hard plasma is to deal with.
Some parameters for typical space Plasmas are; general overall temperature, Particle Density, Magnetic Intensity, Individual component Temperature (Ti) (Te), and magnetic moment. These are given by the table as follows:
|5000||50||10||3 x 10^6||5 x 10^-9|
|10000||1000||1||1 x 10^9||5 x 10^-7|
|10||0||0.02||1 x 10^12||-|
|40000||-||-||1 x 10^3||-|
One big problem plasma data has is it depends upon what book is read. These figures were derived from sources at NASA and from what I consider a good book on plasma; Introduction to Plasma Physics and Controlled Fusion by Francis F. Chen. Another book recommended by the U.S. Department of Energy; Principles of Plasma Physics by Nicholas A. Krall & Alvin W. Trivelpiece.
Many feel the study of plasma physics is the study of wave gyration. The light weight electron is gyrating with grater intensity about its center. The more massive proton is gyrating about its center too. Both gyrations are spherical in nature and depend upon electric, magnetic, electromagnetic and gravitational fields in which the gyrations are occurring. These gyrations are normally called frequencies.
In the world of Thermal Dynamics the energy required to expand the electron and proton's sphere of influence is called the temperature. The development of thermal dynamics is really approximations and probabilities. The electron has a temperature of Te and the proton can have another temperature of Ti (i for ion). Generally, temperature is the degree by which the particle vibrates. The hotter the particle the more it is vibrating. Temperature is mostly understood in degrees but it is also given in electron-volts (eV). [1 eV = 11,600 degrees Kelvin]. All one can say when evaluating the theory of Thermal Dynamics plasma's particle temperature is that for any given area of approximation, there is a numeric probability that the particle is present. Plasma is any element excited beyond its rest state. The degree of excitement is temperature.
Besides the electron and proton being excited the relationship between the two is different and this is called the overall particle energy, frequency or temperature. These different properties exert some force on whatever media they are going through. A plasma beam which is going through a magnetic field will experience a force. If the speed is fast enough and the magnetic field is strong enough, then trapping forces will hinder one of the particles which intern generates a force on the opposite polarity particle. The ratio of neutral and forced separation is the Lorentz force.
The Lorentz force:
Plasma itself creates a pressure. This pressure is in the form of magnetic influence and exerts a pressure on the environment. This pressure is the result of a force similar to that of a cup sitting on a table only it is magnetic instead of gravity. The Lorentz force is affect on a particle by the environment and the magnetic pressure is in effect the counter force by the particle on the environment.
Plasma itself is basically diamagnetic. The effects of its diamagnetic properties depends upon the ratio between particle pressure and magnetic field pressure.
Typically, a low pressure ratio is between 10^-3 and 10^-6.
Generally, plasma opposes the development of a magnetic field.
Like most magnetic fields there is a moment associated with a plasmatic particle. Magnetic moment:
Plasma is mostly nonlinear however, most formulas are linear. Plasma can have the condition where two or more particles can be going in different directions independently in one mass. All the forces on plasma have both static and dynamic conditions which result in many wave structures. Such as; light, electrostatic ion, hydromagnetic, magnetosonic, magnetic shock, acoustic, (L,R,O&X), and Alfven waves.
The general force formula for electromagnet effects on plasma is:
The basic field equations are known as the hydromagnetic equations and are generally approximations. Generally, these are fluid equations. As a fluid, plasma travels, consequently all the magnetic moments add up, creating magnetic pressure in all directions. This is three degrees of freedom depending upon magnetic field intensity. Therefore, this is a stress tensor.
Plasma acts as a fluid and as a charged body. An effect of plasma as a fluid is the ability to neutralize a charged body. If a charged body is placed in a plasma, and it was of a nature not to give up its charge to the plasma, then the plasma would shield the charge by oppositely charged particles gathering in a cloud around the charged body. This phenomenon is called Debye shielding. Because the charged body and plasma are two different medias, there is a distance within the plasma that the neutral charge affect. Greater than that distance, the charged body is affectively isolated. This distance is the Debye length and give by:
The Debye shielding effect is only valid if there are enough particles in the charge cloud to effectively neutralize the charge. If there are only one or two particles in the sheath region, Debye shielding would not be statistically valid. For solar space quite a distance from Earth, the Debye length is typically 100 to 400 meters. Closer to Earth the Debye length can be as short as 2 to 50 meters. In the reaction area of the Sun it is in millimeters. Either values, compared to the distance from Earth to the Sun, the Debye length is insignificant. When compared to a nuclear reaction within the proton-proton space, the Debye length is also invalid. There is both enough particles in the hugeness of solar space, and sufficient distance to insulate any charge on an astronomical scale.
Plasma is a good conductor. As with all conductors, plasma has a resistance to current flow. Taken from Francis F. Chen's Plasma Physics, plasma has its spatial resistivity shown by Spitzer and is given by:
This formula was generally reduced by Spitzer for hydrogen as:
The resistance depends upon the motion of the particle with respect to the magnetic field. However, this resistance acts not much differently than the common resistance found by Ohm. At nuclear temperatures this formula breaks down because the ohmic heating gets very slow. Also, the perpendicular resistance isn't just twice the parallel resistance. Cyclotronic motion must be taken into account.
Typical values which approximate hydrogen resistivity are: (Cu = 2 x 10^-8 ohm-m)
|1.1 x 10^-4 ohm-m|
|3.7 x 10^-6 ohm-m|
|3.3 x 10^-7 ohm-m|
|1.1 x 10^-7 ohm-m|
|3.7 x 10^-9 ohm-m|
|1.1 x 10^-10 ohm-m|
Resistivity depends upon many different factors in plasma, the velocity, temperature, the magnetic field, the element and density. When a current moves through plasma it follows the standard Ohms's law relationship for power P = R*I.
There is the cyclotron energy which is required to alter the particles guiding center. This is referred to as the cyclotron frequency and is very dependent upon perpendicular magnetic flux:
The cyclotron frequency radius called the Larmor radius is:
In an electric field the particle guiding center will drift with velocity:
This causes the particle to travel with a three-dimensional helix trajectory, which is changing pitch as it travels and bending. As the magnetic field or particle velocity changes, the Larmor radius, helix trajectory, magnetic pressure, and energy required to drive this affect changes.
The faster the particle goes, the more drag on the particle. The theory is, as the plasma moves through the magnetic field the electron is greatly affected because it has far less mass. The affect on the electron is to make it go around the helix faster, making it take more energy to go around in circles than go forward for a give time segment. This creates a breaking effect on the forward motion of the electron. Because plasma still is a complete particle, the electron is held back, thus, there becomes a coulomb force which slows the proton. Since both are held back, it is drag on the total particle.
Plasma civitates just as other fluids too. Cavitation in water is typified by a steam trail from a high speed object such as a bullet fired into water or a propeller on a boat. Cavitation is an immense form of drag. In water it is caused by the inability of water molecules to replace those moved away. When one figures it requires an enormous amount of energy to create a state change in water, the breaking force is very great. To sailors one quickly finds that a stationary prop under sail offers less resistance to one which is spinning and cavitating. Plasma, cavitation is less pronounced but in effect, not much different than the same affect in water. It is the creation of a hot spot down stream from the obstruction in the flow of plasma. The hot spot can be very hot.
As more particles are introduced, the helical trajectory creates a plasma pressure. The plasma pressure has several components; those components which are physical and those which are electromagnetic. Both are strongly influenced by electric and magnetic fields.
So strong can be the effects of the electromagnetic fields that particles can be trapped. In many cases the trap can be of a type that actually allows the energy of the trapped particle to increased, thus, creating a thermal amplifier. The amplifier can pump enough energy into the plasma particle to become relavistic and radiate. Such is the case with the Van Allen belt and the Northern Lights.
Plasma energy gives rise to two different shock types. Those surfaces of discontinuity which correspond to different elements, and those surfaces of discontinuity which correspond to different plasma energies of the same element. The latter is the case of the Bow Shock from the Earth plowing through the solar plasma.
Applying the thermal relationship of energy to pressure and density:
With the Earth's Bow Shock, there are drastic changes in plasma temperature between outside the bow shock, and inside there is little changes in the pressure and density ratio. Since plasma's energy is also dependent upon magnetic flux, there must be a magnetic flux change which gives rise to magnetic pressure.
To maintain relative equal pressure requires the Larmor radius to be equal therefore:
Since m, q and density are the same:
This suggests, plasma particles, like the solar wind outside the sheath surrounding the Earth being of high energy, would be traveling very fast and have a low magnetic flux, where as, the particles inside the sheath would be traveling slow and have a large magnetic flux. This seems to be the case with the Earth's bow shock. A strong magnetic field inside the sheath dramatically deflects the high speed solar wind particles at a very sharp boundary in space surrounding the Earth. So, math and reality seem to correlate as the Earth flies through a very hot plasma. The plasma itself, protects the Earth from the extreme temperature. Somewhat like the Ozone protects the Earth from ultraviolet rays which are striking the Earth in the upper atmosphere.
To generate a magnetic field, work must be performed. Normally this work is in the form of current flow however, it can be in the form of mechanical energy too. The mechanism for such a shock wave is acoustic in nature and cause by supersonic velocities. The wave is analogous to that of the sound barrier on Earth. One parameter which is used is the Mach number of the shock.
Because the electrons are more mobile than the ions, they speed up and slow down about a point of oscillation. As the plasma flows in a direction 'X' electrons bunch up creating potential waves which travel with a velocity parallel to the plasma flow. This is the plasma frequency and is given by:
Introducing the term propagation constant k which is the ability of the plasma to propagate a wave. Two significant velocity values can be generated. One is called the phase velocity and the other is the group velocity of the wave. Phase velocity = vp = change in distance x (dx) per a change in time (dt) = wave frequency divided by the propagation constant:
Group velocity = change in frequency (df) per change in propagation constant (dk).
Adding the effects of thermal electron motion to the electron plasma frequency gives a complex wave of frequency:
The basic term for this is instability. The mechanism is the difference in mass creating a difference in mobility. Electrons move out fast, leaving a positive charge bunch. As the electrons and proton separate coulomb forces take affect and electrons are attracted from the opposite side creating: negative-positive-negative-positive bunches.
The work relationship for waves in plasma is given by:
Since the change in energy for a wave propagated in plasma is dependent upon frequency, it averages to zero. Also, note, that as the velocity times the propagation constant approaches the resonant frequency, the work in any given instant of time increases by a power cubed. < p> Further refinement of the Bohm-Gross dispersion relationship for fluid plasma waves yields:
making a = 1, An a constant, and Bn = 0; yields the same old Bode-Titus series. Looney-Brown (1954) showed this type of oscillation relationship to exist in microwave the range.
For frequencies which are close to resonance the work can be broken up into two parts; that which is electrical and that which is kinetic and this affect is called Landau damping.
Simply, Landau damping is the limit of the energy build-up as frequencies approach a resonant point.
Work must be done:
Plasma does not always do what is expected. For example; an experiment by Lindberg and Kristoferson in 1971 showed, that when a plasma pulse moving parallel to a magnetic field reached a point where the field bent, the plasma may bend in the opposite direction. This is contrary to the standard plasma-magnetic theories. This is also subject to some unknown as the word may is very important. At various energy levels, the pulse moved opposite to the field and others it moved parallel to it.
Lindberg and Kristoferson's experiment tends to disprove the theory that the plasma particles leaving the Sun are following the magnetic line out into space. Also, this experiment tends to support the theory that the Sun's outward (plate type opposed to the dipole) magnetic field is the result of work rather than doing work.
A sufficient external magnetic force can be applied to the plasma, to cause the plasma virtually stop and reverses direction. Such is the case with magnetic mirrors used in Plasma heaters, guns, and the Earth's Van Allen belts. In effect, this is throttling using magnetics to regulate plasma. The mechanics of plasma particles in a mirror; as the plasma particles gyrate in three dimensions, when the external magnetic field is applied, the particles change vibration, and reflect off the trapping magnetic field.
Two interesting pulse amplification system can be developed from magnetic throttling. One is the acceleration of a plasma particle trapped between two converging magnetic mirrors. The result is increased velocity of the particle until the magnetic trap can not hold the particle and it escapes. This is the same effect as shaking a long thin flexible rod and moving your hand down the rod, the vibration increases. The other type of amplification is stimulated emission. This occurs when the density of the trapped particles goes up and the particles become close enough to excite each other. One particle will give up its energy to another thus, pumping up the gifted particle. When the pumped particle gets sufficient energy, it will radiate the energy in the from of an electromagnetic wave. Such is the case with Lasers and the Aurora.
Due to the helical trajectory of plasma, electron mobility and force alignment a wave perpendicular to the drift with a velocity of:
A function of velocity and mobility is that of the mass. Generally speaking, it is easier to affect the electron than proton. This graph shows the electron can be moving in any direction while the proton is only affected in the positive direction of velocity. fi is ion or proton bandwidth and fe is that of the electron.
In terms of bandwidth, this graph also shows that electron frequencies are much wider than proton frequencies.
As plasma streams by the Earth, the effects of the Earth on the plasma is seen in the plasma trail. Applying the torque vector, one can also expect the tear in the plasma stream to twist as it leaves the influence of the Earth. If the influence vector is on the tear, then the thumb would point toward the Sun, and the twist on the tear would be in the direction of the curl of fingers. If the influence vector is caused by the tear, then the thumb would be pointing away from the Sun, and the curl of the fingers would indicate the twist of the tear. Deep space measurements bear out the twist of the tear and it is with the influencing vector pointing away from the Sun.
Plasma mixes and adds waves. For example; plasma echoing. In a column of plasma moving at a constant velocity which has a plasma wave injected in it with frequency f1, that allows for a fast Landau damping at X; a second plasma wave injected with frequency f2 at distance L from X down stream, an echo at Le = L * f2/(f2 - f1) will appear. The reason for fast Landau damping is to detect a wave perturbation easily. This occurs only for f2 > f1. Echoing is also constant with the electromagnetic theory and the mixing of waves.
Another example of plasma wave mixing is R-waves and L-waves. This occurs as the phase velocity and group velocity become zero at the resonance point of the fundamental frequency. At which time the particle changes from electromagnetic to electrostatic oscillation. Two other waves which can interact are Ordinary waves and Extraordinary waves. Ordinary waves are those which propagate with an electric field oscillation both planes of oscillation and the electric field oscillates circularly. Extraordinary waves are those wave with an elongated electric field, such that the electric field oscillates elliptically. Still another wave form of plasma discontinuity is that of a column plasma contained and area beside the plasma parallel to the flow of particles. The terms for this discontinuity is fringe effect or potential well.
All that can be derived from this quick chapter about waves in plasma is, it can be said, plasma propagates electromagnetic waves very easily.
What humanity knows about space is very limited. We do know that solar space is a plasma. We can say two things for sure about solar space; 1. Solar space is spherically unbounded. 2. Solar space changes density proportional to the inverse square of the distance from the Sun. What we do know about solar space is very limited.
Although, both the U.S.A. and U.S.S.R have sent explorers to deep solar space, the measurements have yet to show exactly how large the electron current flowing away from the Sun is. We have made several measurements which seem to indicate some-sort of electron flow but we aren't sure why. Since, theoretically, an uneven flow of electrons to protons away form the Sun, given long enough time, would create a large coulomb force, holding electrons captive by the Sun. This electron current flow is said to be impossible. However, our measurements say it is happening. Then again, we have no idea what is happening in solar space above and below the Sun. We have little knowledge about the make-up of inner-planetary space and no knowledge about galactic space.
Without many more measurements of solar space, formulas explaining the exact nature of electromagnetic waves in solar space are premature. All that is necessary to support this theory is that electromagnetic waves of the nature given are possible. It comes down to simply choosing an appropriate propagation constant.
It wasn't till about 20 years ago did humanity find out that solar space was a plasma. It was always considered a void. It turns out that solar space is far from a void. Solar space is hot, conducts currents, highly magnetic, and has density.
With regard to solar space, we are but like Christopher Columbus proving the Earth was round. Captain Columbus never proved the Earth was round, he only proved that it arced. It took Captain Cook, aboard the Endeavour, to go far enough west to prove the Earth was round.
The same is true working with solar plasma. Plasma in a test tube, under gravity, at a constant pressure, in a constant magnetic field, and bound is far different than solar plasma. Solar plasma is not bound by sides of a jar. Solar plasma is a continuous fluid type substance surrounding the Sun. Solar plasma's particle pressure undoubtedly changes as the distance from the Sun changes. Solar plasma's magnetic pressure is probably different for greater distances from the Sun too. It's possible, but not likely, the same thermal temperature and particle velocity can be maintained all the way out past pluto. There is yet a lot to be discovered with solar plasma physics.
TABLE OF CONTENTS
LAWS & THEOREMS
ONE HOT GLOB
THE SOLAR ENGINE