Contents: 1. Introduction 1. 1 Basic Physics of Charged Particles Moving In a Magnetic Filed 1. 2 The Lorentz Force 1. 3 The Hall Effect 2. What Is Plasma? 2. 1 What is it that distinguishes plasma from ordinary gases? 2. 2 Commercial Applications 2. 3 Waves in Plasma 3. Nuclear Fusion & Fusion Reactors 3. 1 The Lawson’s Criterion 3. 2 Magnetic Field Confinement 3. 3 Inertial Confinement 4. TFTR & Its Contributions to Engineering 4. 1 Transport 4. 2 Fusion Power Production 4. 3 Alpha-Particles Physics 5. Plasma & Space 5. 1 Solar Prominences . 2 Plasma Rockets 6. Conclusion 7. References Table of Variables & Constants: ?0Permittivity of free space kCoulomb Constant, 9? 109 N m2 C-2 ?Efficiency ?Confinement time ?Angular frequency vVelocity qCharge mMass eElectron charge UPotential energy FForce BMagnetic field PPower EElectric field VVoltage TPeriod or Temperature 1. Introduction: Until recently, looking at pictures similar to the one above had caused me to wonder; could this be a creation of some proficient artist, or the work of a powerful computer program?
Honestly I never thought that this luminous phenomenon appearing as streamers of light, usually seen in the northern and southern regions of the globe, is what we have been taught in freshmen and sophomore physics about plasmas. The aurora visible in this picture is thought to be formed by charged particles from the sun entering the earth’s magnetic field and stimulating molecules in the atmosphere. In one of the courses that I attended last semester, the instructor asked the class the following question; what is the greatest source of plasma noticeable to us?
Among the seniors that were in that class, I, the first semester junior student, was the one who answers the question. Although I knew that our sun consists of plasma, I never really understood what the existence of plasma is all about. Fortunately, that class was concerned with direct energy conversion and its applications. Moreover, one of its essential topics was plasma and its essence in this field of studies. For some reason that I cannot really figure out, the sun is a great source of inspiration for me. I get really astonished by any new fact that I learn about the sun.
In this paper, I tend to present some of the phenomena that are of relevance to the study of plasma. Mainly, this paper is designated for the field of plasma confinement, which in turn requires an adequate knowledge of the physics of nuclear fusion. 1. 1. Basic Physics Of Charged Particles Moving In A Magnetic Filed: If a charged particle moves in a uniform magnetic field, it will be subjected to a magnetic force acting in a perpendicular sense to its velocity. Thus, the work done by this force is zero because the displacement of the particle is always perpendicular to the magnetic force.
Therefore, a static magnetic field only changes the direction of the velocity and has no effect on the speed of the charged particle. Considering the case of a positively charged particle, of magnitude q, moving in a uniform external magnetic field with an initial velocity of v, whose vector is perpendicular to the magnetic field directed into the paper. Obviously, the particle will undergo a circular motion perpendicular to the magnetic field as shown on the above figure. If we are to get into more details, the magnetic force is at right angles to the velocity, and B, the magnetic field, and possesses a magnitude of qvB.
While the force is deflecting the particle, the directions of v and the force, F, change continuously. Hence, the magnetic force in this case is a centripetal force. We can notice the effect of this force in keeping the speed at a constant value. If we wish to relate this magnetic force to the centripetal acceleration by Newton’s second law of motion: F=qvB= mv2/r r=mv/qB Hence, the radius of the path is directly proportional to the momentum of the particle and inversely proportional to the magnetic field. Anyway, the angular frequency for the rotating charged particle is found by: ? v/r=qB/m The period of this motion is easily found by dividing the circumference of the circle by the speed of the rotating particle: T=2? r/v=2? /? =2? m/qB The results above show that the angular frequency and the period do not depend on the speed of the particle or the radius of its orbit. This angular frequency is often known as the cyclotron frequency since charged particles circulate at this frequency in one type of accelerator named a cyclotron. If a charged particle moves in a uniform magnetic field, with its velocity at some arbitrary angle to B, its path is a helix.
For example, if the field is in the x-direction as in the figure shown below, there will be no component of force in the x-direction, and hence ax=0 and the x component of the velocity vx remains constant. In contrast, the magnetic force qv? B causes the components vy and vz to change with time, and therefore the resulting motion is a helix having its axis parallel to the magnetic field. An even more interesting fact is when charged particles move in a nonuniform magnetic field. Here the motion is rather complex.
For instance, in a magnetic field that is strong at the ends and weak in the middle, the particles will be fluctuating back and forth between the ending points, as in the figure shown below. Anyway, this magnetic field can be generated by two current loops going in the same direction. In this case, the charged particle will start spiraling along the magnetic field lines starting from one end till it reaches the other end, where it reverses its path and spirals back again. This model is known as the magnetic bottle because it has the capability of trapping the charged particles in it.
This concept is very crucial in this context because it has been used in order to confine extremely hot gases, where the temperature is greater than 106 K. This is of course our subject of interest, the plasma. However, this plasma-confinement scheme could play a vital role in achieving a controlled nuclear fusion process, which could of course supply us with an infinite amount of energy. The Van Allen radiation belts consist of charged particles (mostly electrons and protons) surrounding the earth in doughnut-shaped regions as shown in the figure below.
Here, the charged particles, trapped by the earth’s nonuniform magnetic field, spiral around the earth’s field lines from one pole to the other. Anyway, these particles originate from the sun or from other stars. Because of this, these particles are given the name cosmic rays. Most cosmic rays get deflected by the earth’s magnetic field and never make it to the earth. However, some of them get trapped and form the Van Allen belts. When these particles reach the earth’s atmosphere over the poles, they collide with other atoms, causing them to radiate visible light.
This is origin of the Aurora Borealis, or Northern Lights. A similar phenomenon seen in the southern hemisphere is called the Aurora Australis. 1. 2. The Lorentz Force: In many situations, the charged under consideration will be moving with a velocity v in the presence of both an electric field E and a magnetic field B. Hence, the charge will be experiencing both and electric force qE and a magnetic force qv? B, and therefore the total force on the charged particle will equal: F= qE+ qv? B The previous equation describes a special type of force called the Lorentz Force. . 3. The Hall Effect: In 1879 Edwin Hall discovered that when a current-carrying conductor is placed in a magnetic field, a voltage is developed in a direction perpendicular to both the current and the magnetic field. This observation was later known as the Hall Effect. This effect arises from the deflection of charge carriers to one side of the conductor as a result of the magnetic force experienced by the charge carriers. A proper analysis of experimental data gives information about the sign of the charge carriers and their density.
The effect also provides a convenient technique for measuring magnetic fields. +y +z+x The arrangement for studying the Hall Effect consists of a conductor in the form of a flat strip carrying a current I in the direction shown in the figure above. A uniform magnetic field B is applied in a direction perpendicular to the strip. Let us assume that the charge carriers are electrons moving in a direction opposite to the current, and have a velocity of vd . By the right-hand rule, the magnetic force should be directed to the positive z direction. Hence, the electrons will be deflected in that irection and accumulate in that part of the strip. As a result, an excess amount of the positive charges will accumulate in the opposite side of the strip. This accumulation of charges will continue until the electrostatic field set up by this charge separation balances out the magnetic force on the charge carriers. When this equilibrium condition is reached, the electrons will no longer be deflected. Notice that the direction of the magnetic force is dependent on the charge carrier; in our assumption we chose the electrons to be the charge carriers.
If we chose positive charge carriers that are flowing in the same direction as the current, the magnetic force will be directed to the negative z sense. However, if we connect a sensitive voltmeter or potentiometer across the sample shown above, a potential difference will be measured, which is called the Hall Voltage, VH. To find an expression for this voltage, first note that in equilibrium, the magnetic force is balanced by the electrostatic force qEH, where EH is the electric field due to the charge separation: qvdB = qEH EH = vdB
And if d is considered to be the width of the strip, then the Hall voltage measured by the potentiometer is equal to: VH = EH d = vdBd Thus, we see that the measured Hall voltage gives a value for the drift velocity of the charge carriers if d and B are known. If we want to calculate the charge density, n, we need to measure the current in the sample. Since the drift velocity can be expressed as the following: vd = I/nqA where A is the cross-sectional area of the conductor. Therefore, the Hall Voltage can be expressed as follows:
VH = IBd/nqA The quantity 1/nq is referred to as the Hall Coefficient RH. 2. What Is Plasma? As I previously mentioned, the earth is covered by streams of plasma. Solar activity drives an outward stream of plasma as well known as the solar wind. Some of the charged particles are trapped in the earth’s magnetic field creating structures known as the radiation belts, shown on the above picture. Plasma is often referred to as the fourth state of matter in order to distinguish it from the common three states to us.
It actually forms more than 98% of the visible universe by some estimates. This state of matter is dominant in the atmospheres and interiors of stars, the wind of particles that the sun flings out into the space, the earth’s magnetosphere, the wasteland between stars and galaxies, supernovas, and parts of the compact spinning stars that spray out streams of x-rays. Plasma can be artificially produced and bottled up, and this fact has actually found itself a great deal of applications. Plasma is created each time we flip on a fluorescent light or a neon sign.
Plasmas also etch the tiniest circuit features on the microprocessor chips that are the heart of every computer. Carefully controlled clouds of plasma are used to deposit thin layers of materials onto surfaces as an essential step in manufacturing superconducting films and diamonds. In particle accelerators, intense plasma waves are used to speed up the electrons to relativistic velocities. However, laboratory experiments help shed light on the greatest plasma phenomena, as when shock waves produced by laser beams striking a small speck of plasma expose the dynamics of an exploding star.
After decades of hard work, scientists have learned how to confine plasma at temperatures that are hotter than the sun’s core, with the aim of providing large power plants with the energy needed. 2. 1. What is it that distinguishes plasma from ordinary gases? Plasma sometimes is defined as an “ionized gas”. This concept is what distinguishes it from the ordinary neutral gases. Every atom has the same number of negatively charged particles orbiting the nucleus. While an ordinary gas usually possess plenty of chemical activity along with dynamical effects, such as fluid turbulence, it shows very little response o either electric or magnetic fields, and is somehow incapable of conducting electricity. The gas jumps to life once enough of its atoms have undergone ionization. This ionization sometimes takes place because the gas is very hot, its atoms smash together jarring loose electrons. These electrons virtually never encounter an ion with which they recombine, possibly because the system is subjected to an outside source of energy, such an electric field very strong it rips the electrons from atoms.
Anyway, the resulting plasma consists of interpenetrating, and interacting clouds of roaming charges whose motions both generate electromagnetic fields and are, hence, influenced by them. How fast can a change in properties occur? The properties of a gas can be shifted from neutral to plasma with lightning quickness. In thunderclouds, the churning winds can charge up parts of the clouds, either positively or negatively, with respect to ground. When sufficient charges build up somewhere, it can drive a weak branching electrical discharge that is driven invisibly towards the ground.
As soon as one of the branches touches an object, the excess charge blasts through the electrical connection, ionizing and heating the atmospheric gases along this path. The tremendous heat generates a shock wave creating the sound known as the thunder. If we need to check the presence of plasma, we have to test the tendency of a cloud of charged particles to gather up and “shield”, or form an electrostatic sheath around any particular charged object that is placed in the vicinity of this cloud. This object could be an ion that is singled out from the rest of the cloud.
However, in a vacuum or a normal gas, the electric field around the ion falls off approximately as the square of the distance from the ion. But in plasma, the field is nearly completely shielded beyond a distance called the Debye Length. In fact, it is only when the Debye shielding length is smaller than the cloud of charged particles, which the physicists strictly refer to the collective ensemble as plasma. By this criterion, plasma can coexist with a background of ordinary gas, flowing through, and interacting with it via collisions only.
More technically, the more charged particles per unit volume are present to neutralize the electric fields, the shorter the Debye length; and the higher the plasma’s temperature, allowing its particles to resist the temptation to assemble around a bare charge, the longer the Debye length. The key however, is the notion that particles in plasma behave as a collective beast that seems to have a mind of its own. Now, how can we develop an expression for the Debye shielding distance?
Consider a homogeneous and electrically neutral mixture of atoms, molecules, electrons, and ions at high temperatures to be the plasma. This neutral plasma view breaks down on a size scale of the individual ions and electrons. In fact, it breaks down on a larger scale because the plasma components’ kinetic energy is sufficient to separate charges against the electrical field. This scale is of interest, given the fact that we want to consider its relation with the physical dimensions of the system wherein the plasma is contained.
Maxwell’s equation, which describes the electric field, allows estimating the magnitude of the field that can be set up by separated charges and thus the work required to bring that about. The work must be supplied from the thermal energy of the plasma components. Actually, this reasoning allows us to identify a length scale dividing the spectrum of possible charge separation distances into a small-scale regime where one could expect positive and negative charges to be separable, and a larger-scale regime where there is insufficient thermal energy for this separation to take place.
Consider a plasma that is uniform except that a slab of thickness h, infinite in extent in the remaining directions, contains no electrons. The figure below actually explains this situation; the slab that was shortly mentioned is the one contained between the two planes of neutral plasma, the orange and the gray planes. The region in between consists of ions only that have a uniform density. However, if we take x to be in the region between 0 and h: dEx/dx = ne e/? 0 This equation can be integrated, once to find Ex, and twice to obtain the potential at various locations between 0 and h.
Hence, with Ex (0) = 0, Ex = x ne e/? 0. The potential at x = h relative to x = 0 is: ? = (ne e/? 0) (h2/2) However, this potential multiplied by the electronic charge is the work required to bring a charged particle across the gap h. The thermal energy available in one dimension to move this particle is ? kT, where k is the Boltzmann’s constant. Equating the work required to the energy available allows us to know a length scale h over which charge separation will be found. e ? = kT = (ne e2/? 0) (hD2/2) Hence, the Debye shielding distance has the value of: D = (? 0 kT/ ne e2)1/2 Neutral Plasma Neutral Plasma x Ions Only, Uniform Density 0 h x ne 2. 2. Commercial Applications: As a demonstration of the behavior that was shortly mentioned, a skin or sheath is formed around plasma when it is in contact with a solid surface. Space charges have important consequences near boundaries of the plasma, or the sheath. Plasma sheaths, like many other collective effects in plasma, can be either a curse or a blessing to engineers who try to put this state of matter to work out for the best.
When plasma is created above a wafer, a thin circular slice of a semiconducting material on which an integrated circuit is placed, in a microprocessing fabric, the strong electric fields in the sheath at the wafer’s surface accelerate the plasma ions downwardly. Hence, some of these ions zip through the gaps in a “photoresist” that bears the pattern of the integrated circuit. Those ions however crash into the silicon-based material and pump energy into the chemical reactions that etch the narrow and deep trenches, often less than a micron, out of which the circuits are made of.
Earlier methods that were based on wet chemistry tended to undercut the trench walls and hence could not carry as much memory and logic circuitry onto a wafer. On the picture below, we can see how plasma etching is used to fabricate high-density integrated circuits. A microscopic blowup of the etched surface is shown on the upper right corner. 2. 3. Waves in Plasma: A neutral gas only supports sound waves, due to the seesaw competition between the neutral atoms’ pressure and their inertia when the gas is jostled at the right frequency.
These sound waves eventually die away as collisions between the atoms turn its coherent motions into random thermal energy in the gas. Plasma, on the other hand, supports a multitude of wave motions. The two simplest waves are called Langmuir and ion-sound waves. In the first of these two waves, the ions are nearly stationary and the electrons rapidly oscillate around them like pendulums. The force that swings the electrons back and forth is due to the strong electric field that temporarily builds up when the negative charge in the local cloud of electrons does not balance the positive charge of the ions.
Hence, the oscillations, as the disturbed electrons rush back to short out the field, overshoot and rush back again. The lower frequency ion-sound waves behave almost like the usual waves in neutral gases, with one crucial difference: the waves’ speed is determined by the ion’s inertia and the combined pressure of both species. In this wave, the ions and electrons swing in synchrony, fastened together by the electric field that comes about when one of the species lags slightly behind in the thermomechanical swing.
Most remarkable and astonishing of all is the ability of the plasma to damp away its waves when collisions between particles are negligibly rare. This collisionless damping occurs when some of the plasma particles are moving with a velocity close to the same velocity as the waves phase themselves, so that the particles ride this disturbance just like a surfer on a water wave. The particles gain energy while the wave loses energy and damps away. In this way, a wave maybe considered to be “heating” the surrounding plasma. In terrestrial laboratories, experimentalists call on a similar effect to accelerate bursts of electrons to high energies.
The concept is to excite large amplitude Langmuir waves by firing super intense pulses into plasma. However, the laser pulses have pressures that shove the electrons out of the way. We could think of the pulse to be some sort of a speed boat, and in its wake are huge waves whose electric fields are used to accelerate electrons to high energies. Surprisingly, these fields are so strong they are capable of tearing apart some material structures; particles accelerators based on this effect could be both more powerful and way smaller than those that use conventional technologies. 3.
Nuclear Fusion & Fusion Reactors: The nuclear fusion is the process that involves the combination of two light nuclei in order to form a heavier nucleus. Because the mass of the resulting nucleus is less than the combined rest masses of the two original nuclei, a loss of mass takes place, and therefore a tremendous amount of energy is released. Below is a schematic of what goes on in a fusion reaction These are the basic reactions in what is called the proton-proton cycle. They are considered to be one of the basic cycles by which energy is generated in the sun and other stars with an abundance of hydrogen.
Most of the energy production takes place inside the sun, where the temperature is about 1. 5? 107 K. Thus, one may conclude that such high temperatures are necessary in order to drive these reactions. The reactions illustrated above are very exothermic, that is, there is a release of energy. Usually, the release of an alpha particle and two positrons is accompanied by the release of 25 MeV of energy during the process. The enormous amount of energy produced in fusion reactions suggests the possibility of harnessing this energy for constructive purposes.
Efforts have been spent on developing a sustained and controllable a fusion power reactor. Controlled fusion may be promising because of the availability of its fuel: water. If deuterium were used as the fuel, 0. 12 g of it could be obtained from 1 gal of water at a cost of about 4 cents. Moreover, this source of energy has the advantage of comparatively few radioactive by-products. As seen on the picture above, the ending product of the fusion is safe, nonradioactive helium. Unfortunately, a thermonuclear reactor that an deliver a net power output over a reasonable time interval is not yet accomplished. Again, we all know that sun’s energy is based on a set of reactions in which hydrogen is converted to helium. Unfortunately, this event requires very high pressures and densities. The process works perfectly in the sun’s interior because of the extremely high density of protons that are present there. A major problem with extracting energy from nuclear fusion is the fact that the Coulomb repulsion force between the charged nuclei must be overcome before they can combine.
How can we give the nuclei enough energy to overcome this repulsive force? This can be accomplished by heating the fuel to extremely high temperatures (to about 108 K, which is even greater than the temperature of the interior of the sun). Such temperatures are indeed not easy to obtain in the laboratory or a power plant. At such temperatures, the atoms are ionized, and the system consists of a collection of electrons and nuclei, which is again our subject of interest. How can we estimate the temperature required to cause the fusion of two deuterons?
The separation between two deuterons must be as little as about 10-14 m in order for the attractive nuclear force to overcome the repulsive Coulomb force. First, we need to find out the height of the potential barrier due to the repulsive force. The potential energy associated with two charged particles separated by a distance r is given by: U = k q1q2/r where k is the Coulomb constant. For this case, the two charged particles are deuterons and both have the same charge of +e, so that: U = ke2/r = 2. 3? 10-14 J = 0. 14 MeV
Now, if we want to estimate the effective temperature required to overcome the potential barrier, we can assume an energy of (3/2) kT per deuteron (where in this case k is the Boltzmann’s constant). Since the total energy of the system combined of two deuterons is 0. 14 MeV, the Coulomb energy per deuteron is equal to 0. 07 MeV. Setting this equal to the average thermal energy per deuteron leads to: (3/2) kT = 1. 2? 10-14 J where k is equal to 1. 38? 10-23 J/K. Solving for T gives a value of 5. 8? 108 K. The previous analysis suggests that the deuterons must be heated to about 6? 08 K in order for fusion to take place. This estimate is considered to be too high, however, because the particles in the plasma have a Maxwellian velocity distribution and therefore some fusion reactions will be caused by the particles in the high-energy “tail” of this distribution. In addition, even those particles that do not have enough energy to overcome the barrier have some probability of penetrating the barrier through tunneling. When all these effects are taken into consideration, a temperature of about 4? 108 K seems to be sufficient to fuse the two particles.
The temperature at which the power generation rate exceeds the loss rate (due to mechanisms that include radiation losses) is called the critical ignition temperature. This temperature for the D-D (deuterium-deuterium) reaction is 4? 108 K. Based on the assumption that E is approximately equal to kT, this temperature is equivalent to about 35 keV. It was also found that the critical ignition temperature for the deuterium-tritium reaction is about 4. 5? 107 K, or equivalently 4 keV only. 3. 1. The Lawson’s Criterion:
In addition to the high temperature requirements, there are two critical parameters that determine whether or not a thermonuclear reactor will achieve its tasks. These parameters are the ion density, n, and the confinement time, ?. The latter is defined as the time at which the interacting ions are maintained at a temperature equal to or greater than the ignition temperature. These two factors must both be large enough to ensure that more fusion energy is released than is required to heat the plasma. In particular, Lawson’s criterion, which states that that a net energy output is possible under certain conditions, must be satisfied.
More specifically, a net energy output requires that: n? ? 1014 s/cm3 (D-T) n? ? 1016 s/cm3 (D-D) According to Lawson’s criterion, plasma is continuously losing energy through braking radiation (bremsstrahlung) by the emission of x-rays. Hence, a minimum requirement for a reactor is that the thermonuclear power is sufficient to replace the losses. John David Lawson derived in 1957 the minimum condition for power balance in a reactor by taking into consideration the combined efficiency thermal to electric energy conversion and plasma heating.
The previous power flow diagram can be used to derive the Lawson’s criterion. As we can see, the total power leaving the plasma is the sum of the thermonuclear power PN, and the power loss, PL. The power PH available to heat the plasma is obtained after energy conversion that operates with ?? efficiency. To satisfy the condition PH = PL, of power balance within the plasma, it is at least necessary that ? (PN+PL) > PL. Moreover, the energy EH required to heat the plasma is proportional to the ion density n, whereas the energy generated by the fusion is proportional to the product n2?.
Net energy is produced when the energy generated by the fusion process, or the thermonuclear energy, exceeds EH. The constants involved can be evaluated under certain conditions. However, when PH = PL, a break-even point is reached. As of 1989, no laboratory has reported the occurrence of the break-even condition. In summary, a couple of conditions are necessary for a successful thermonuclear reactor; the plasma temperature must be very high, the ion density must be high as well for the collision rate between the particles to increase, and finally the confinement time of the plasma must be long.
Efforts have been spent on meeting the Lawson’s criterion at temperatures that exceed the critical ignition temperature. Even though the minimum plasma densities have been achieved, the problem of confinement is yet to be solved. How can we confine plasma at a temperature of 108 K for times of the order of one second? Basically, there are two methods that have been under investigation to confine plasmas; magnetic field confinement, and inertial confinement. 3. 2. Magnetic Field Confinement: Fusion-related plasma experiments sometimes use magnetic field confinement in order to contain plasma.
A toroidal device known as a tokamak was first developed in the USSR in an attempt to contain plasma. The tokamak has a doughnut-shaped geometry. Note that a combination of two magnetic fields is used to stabilize the plasma; a strong toroidal field Bt that is produced by the current in the windings, and a weaker poloidal field produced by the toroidal current. Not only does the toroidal current confine the plasma, it also heats it. The resultant confining field is helical as shown on the figure. However, these helical field lines spiral around the plasma and keep it from touching the walls of the vacuum chamber.
If the plasma is to touch the walls, its temperature will be reduced and heavy impurities sputtered from the walls “poison” it and lead to tremendous power losses. A major breakthrough in the last decade has been in the area of auxiliary heating to reach ignition temperatures. Some experiments have shown that injecting a beam of energetic neutral particles into the plasma is a very efficient method of heating it to ignition temperatures. Click on the following link to get a virtual tokamak experience; (http://w3. pppl. gov/~dstotler/SSFD/).
The picture above shows the inside of The Tokamak Test Reactor (TFTR) operated at the Princeton Plasma Physics Laboratory from 1982 to 1997. The TFTR set a number of world records; a plasma temperature of about 510 million degrees centigrade. This temperature is the highest temperature ever produced in a lab, and even beyond the 100 million degrees required for a commercial fusion. In 1993, TFTR became the world’s first magnetic fusion device to perform experiments with 50/50 D-T plasma, the fuel required for practical fusion power production. Afterwards, TFTR produced about 10. million watts of controlled fusion power, sufficient to supply power for approximately 3000 households. TFTR has also contributed to the studies of alpha particles generated in a D-T reaction. The extent to which energy is transferred from alpha particles to the plasma is crucial to the achievement of a sustained fusion. Another magnetic confinement technique that has received attention is the previously mentioned mirror confinement scheme. The idea of this method is to trap plasma in a cylindrical tube by adding additional magnetic field coils at the ends of the tube.
The increased fields at the ends serve as magnetic “mirrors” or a magnetic bottle for the charged particles, which spiral around the field lines. Hence, this scheme has an advantage of reducing the leakage problem and increasing the ion density of the plasma. 3. 3. Inertial Confinement: This sort of confinement makes use of a target with a very high particle density, and has a very short confinement time (around 10-10 s). Because of the particles’ own inertia, they do not have the chance to move considerably from their initial positions.
The laser fusion technique is the most popular form of inertial confinement. Here, a small D-T pellet, about 1 mm diameter, is hit simultaneously by several focused, high intensity laser beams. This results in a large pulse of energy that causes the surface of the fuel pellet to undergo evaporation. The escaping particles produce a reaction force on the core of the pellet, producing a strong, inwardly moving, compressive shock wave. This wave increases the density and the pressure of the core and hence a corresponding increase in temperature.
However, when the temperature of the core reaches the ignition limit, fusion reactions cause the pellet to explode. Below is a picture that illustrates this process: The picture below is for an accelerator called Saturn, one of the most powerful x-ray sources in the whole world. It has the potential of igniting a controlled laboratory fusion reaction. It uses up to 25 trillion watts of power in order to produce an electron beam current of 1. 25? 107 A. the energetic electrons are converted to x-rays at the center of the machine.
The glow in this photograph is due to electrical discharge in underwater switches as the accelerator is fired. 4. TFTR & Its Contributions to Engineering: After giving a general overview about the Tokamak Fusion Test Reactor, I would like to explore this device more closely. When reviewing the experiments on TFTR, one observes a dynamic interplay between the technology required to create and heat the plasma, including the sophisticated instrumentation to diagnose the plasma, and experiments to both expand the operating boundaries and to study the underlying physics and theories that predict the results of the experiments.
This interaction between experiments, technology and theory has been really crucial to develop the necessary understanding for the advance of fusion science and technology. However, the original project objectives for the TFTR in 1976 were: to demonstrate the production of fusion energy by burning, on a pulsed basis, the D-T fuel in a magnetically confined system of plasma, to study the plasma physics involved in a large tokamak, and finally to gain more experience in the solution of engineering problems associated with large fusion systems that may approach the size of a planned power reactor.
In this section, a review of some of the aspects and contributions from the TFTR will be presented. More specifically, we will discuss the evolution of our understanding through the results from TFTR, beginning with brief figures about the device, followed by a discussion of transport, fusion power production, and finally alpha-physics studies. During the design of the TFTR, one of the outstanding aspects was the choice of limiter material used to protect the vacuum vessel. Simulations of the TFTR discharges showed that the duration of the high confinement phase could be limited by the influx of metallic impurities.
However, experiments with graphite limiters had shown acceptable power handling characteristics and impurity influxes, and hence, the graphite was integrated in the design of TFTR. The TFTR plasma is limited by a limiter on the inboard side composed of graphite and carbon-fiber composite (CFC) tiles mounted on a water-cooled backing plate. A set of poloidal ring limiters composed of carbon fiber composite tiles is used to protect RF launchers on the outboard side that are used to heat the plasma. The limiter can withstand heat outflow from the plasmas of about 30 MW for a single second.
Heating by both neutral beam injection (NBI) and by waves in the ion cyclotron range of frequencies (ICRF) were used on TFTR. The development of the high-power neutral beams was a major technological mission. The maximum power injected into a tokamak in 1976 was a few hundreds of kW though 4. 8 MW was injected into a mirror machine. This neutral beam system was composed of four beam lines, each with three positive-ion sources. The ion sources operated either in deuterium or tritium. The maximum operating voltage was 120 kV and a maximum injected power into a D-T discharge was 40 MW.
Not only do they heat the discharge, these neutral beams are effective means for fueling the discharge. On TFTR, this fueling has been varied from all deuterium to all tritium. 4. 1. Transport: Before the design of TFTR, two important transport concepts were identified. Firstly, classical transport due to Coulomb collisions had been generalized to a toroidal axisymmetric geometry, or what was later called a neoclassical transport. Secondly, turbulent transport due to electromagnetic and electrostatic instabilities had been invoked to explain the observed experimental transport, which was much larger than predicted by neoclassical transport.
One of the essential purposes of TFTR was obtaining data in order to establish the confinement and transport coefficients of a reactor grade plasma. Due to the limitations of the physics based models used at that time, empirical approaches to predicting performance were widely used. However, these scalings were based on outcomes from already existing smaller devices. The model that was used in the design of INTOR (Alcator scaling for the thermal electron diffusivity and ion neoclassical) was very optimistic, while the L mode scaling (based on high-power heating results on smaller devices) was pessimistic for the performance of the TFTR.
The initial high-power heating experiments confirmed the validity and applicability of L-mode (low confinement mode) scaling. In 1986, it was shown that by extensively conditioning the limiters to decrease the influx of deuterium and carbon from the limiters, much enhanced confinement times could be obtained in limiter discharges. These discharges commonly referred to as supershots, have been thoroughly studied on TFTR. Recently, more effective conditioning techniques involving lithium coating of the limiter have been used to further suppress the influx of deuterium nd carbon, and as a result extend the range of operation. Below is a table that provides a couple of parameters from high-performance D-T supershot discharges on TFTR: In review, the discovery of the supershot operating regime was important for two reasons. The first was that it provided a reliable approach to achieving reactor grade plasmas, which was an essential element in demonstrating fusion energy production. The second was that it showed that the empirical scaling laws had limited applicability and could not be used alone to optimize the performance of the facility.
Hence, the need for exploration and development of an understanding of the underlying physics was even more important. With the development of increasingly sophisticated and accurate diagnostics, the characterization and understanding of transport advanced. One of the first studies was made possible by the supershot regime for the value of ? p became large enough that the bootstrap current predicted by neoclassical theory was significant. During Ohmic discharges, the surface voltage was well described by neoclassical resistivity, although the bootstrap current in these discharges was very small.
In the supershot experiments, the change in surface voltage could only be well defined by including the bootstrap current and the beam current as well, which accounted for most of the plasma current in some supershots. However, the availability of co- and counter-directed NBI in TFTR was important in separating the bootstrap- and beam-driven currents. The neoclassical theory was found to sufficiently describe parallel transport along the magnetic field. In TFTR L-mode discharges, the cross-field transport proved to be more challenging.
This transport has some certain characters: 1. The radial transport is governed by turbulent processes such that the electron and ion heat, particle, and momentum transport is much larger than predicted by collisional transport theories. 2. Local transport coefficients [electron heat diffusivity (? e), ion heat diffusivity (? i), and toroidal momentum diffusivity (?? )] all increase strongly with power or temperature. 3. Toroidal velocity profile measurements following off-axis neutral beam njection can be modeled without introducing an inward momentum pinch. 4. It was observed that the energy confinement time is higher in highly rotating plasmas produced by either co- or counter-directed NBI than in equivalent plasmas without balanced NBI injection, indicating that rotation will affect confinement. Core transport in supershot discharges is substantially reduced when compared with L-mode discharges. The global parametric confinement scalings characterizing the L-mode discharges do not describe the trends in supershot discharges.
In supershots, the confinement time remains approximately constant with both neutral beam heating power and the plasma current, whereas in L- and H-mode discharges the confinement is observed to decrease with power and increase with current. Experiments have shown a strong adverse dependence of confinement upon the influx rates of carbon and deuterium measured. Hence, an increased influx of carbon and deuterium is to broaden the density profile and reduce the depth of penetration by the neutral beam. It has also been shown that the energy confinement time is also correlated with the central beam fueling.
However, the results from the transport studies along with the fluctuation measurements suggest a theoretical model for core transport involving electrostatic modes. Since ion dynamics are important, ion-temperature gradient driven mode are candidates. In addition, flow shear, which is believed to be important in the formation of a transport barrier at the edge, is expected to suppress turbulence. Furthermore, the electrostatic turbulence calculation indicates that transport could be affected by the current profile. 4. 2. Fusion Power Production:
The development of good confinement and high pressure were prerequisites for advancing with D-T experiments to study alpha-particles physics and demonstrate fusion power production. However, the discharge with high fusion power on TFTR could be reduced by MHD instabilities followed by a carbon bloom (a sudden influx of carbon from the limiter into the plasma). The total fusion yield from a single plasma pulse on TFTR has reached 7. 6 MJ. This achievement has satisfied the original TFTR objective of producing 1 -10 MJ of fusion energy.
During the design of TFTR, it was hoped that fusion power densities of 1 MW m-3 could be achieved at the center of TFTR with values of Pfusion /Paux approaching the value of 1. Fusion power densities of up to 2. 8 MW m-3 achieved at the center of high-performance TFTR supershots are comparable to or greater than those expected in the International Thermonuclear Experimental Reactor, and exceeded the original expectations. The achieved value of Pfusion /Paux was only 0. 27, which had fallen behind the optimistic projections performed during the design phase.
It was shown that it would be possible to increase the plasma reactivity by neutral beam injection due to beam-thermal and beam-beam reactions. This concept was explicitly taken into consideration during the design of TFTR. Simulations of the neutron production on TFTR have been performed using the TRANSP data analysis code. This code makes use of the measured electron density and temperature profiles, ion temperature profile, and visible bremsstrahlung measurements, in conjunction with other diagnostic and engineering data, such as the beam heating power and source divergence, in order to calculate the neutron source rate from the reactions.
Monte Carlo techniques have been also used to compute the deposition of the neutral beams, and the distribution of the beam ions and fusion ions, such as alpha particles. The beam ions and fusion ions are assumed to slow down classically. The ration of thermal reactions to those from beam-thermal and beam-beam reactions depends upon the density, electron temperature, and some beam parameters. The overall agreement for both the time dependence of the D-T neutron emission and the neutron emissivity profile is decently described by the TRANSP code for TFTR supershot discharges.
Despite the reasonable agreement in D-T discharges, there seems to be a small, but consistent at the same time, difference in the TFTR results from similar D-only plasmas. The TRANSP code predicts the neutron emission in deuterium discharges to be lower than the measured values by approximately 20%. The reason for this relatively small divergence is not yet understood. Even though the agreement is good in supershot discharges, detailed comparisons of the predicted neutron emission with experiment remained to be performed for the reverse shear discharges.
Initial results indicate a discrepancy between the TRANSP predictions and the actual measurements that may be due, in part, to stochastic ripple diffusion. 4. 3. Alpha-Particles Physics: The behavior of alpha particles from D-T reactions is a very fundamental, yet interesting, consideration for the performance of a future D-T reactor. If a significant fraction of alpha particles is not well confined, then the n T ? requirements for ignition will increase; however, the confinement of the resulting alpha ash must be short in order to avoid quenching the reaction.
In addition, if an unanticipated fraction of alpha particles is lost in a reactor and the resulting heat flux is localized, damage to first-wall components will result. The alpha-particle confinement experiments on TFTR are usually discussed in terms of the conventional description of alpha particles typically used in calculating the performance of a new device. In this conventional approach, the confinement of alpha particles is described using three mechanisms: neoclassical processes (single-particle orbit effects); the transfer of power by Coulomb collisions; and the enhanced transport of the alpha ash from the core.
Since the transport of the background plasma is typically more rapid than predicted by neoclassical theory, it is helpful to re-examine the recent results with respect to our conventional understanding. Measurements of the confined alpha particles, using the charge exchange recombination measurements as shown on the graph above, and the loss measurements, indicate that in MHD quiescent discharges the radial diffusion coefficient for alpha particles is very small, and up to ten times smaller than that of the thermal ions.
A predictable explanation is that “orbit averaging” effects, which occur when the ion banana width is large, compared to the turbulence correlation length, reduce the effect of the underlying background turbulence. The good confinement of beam ions in present machines with smaller orbits than those of fusion products supports the hypothesis that the alpha particles should be well confined in large devices. On the graph above, the absolute intensity measurement of the charge exchange ecombination signal for low-energy alpha particle is shown as a function of the minor radius. We can see that it is in good agreement with TRANSP calculations indicating good radial confinement. Monte Carlo calculations have predicted that first orbit losses are quite small, approaching 3% only, at high current in TFTR, and should not be important in larger devices. However, the implications of the observation of partially thermalized alpha-particle loss are not well understood.
Measurements of the confined alpha particles, as well as loss measurements, predict the presence of stochastic ripple diffusion, which is expected to be larger than first orbit losses. Difficulties in the interpretation of the loss measurements have not made possible a quantitative comparison between theory and experiment and highlight the need for more computational improvements to calculate the loss in realistic geometries. The agreement between the measured alpha-particle energy spectrum and theory indicates that the transfer of power is decently described by Coulomb collisions and orbit effects.
These results are also in agreement with the observations of beam-ion thermalization on TFTR in D and D-T plasmas, as well as many other devices. However, it should be noted that such measurements only sample a small fraction of the distribution function of alpha particles. Alpha-particle heating is small in TFTR plasmas, and cannot be used to obtain an accurate assessment of the power transferred from the alpha particles. Another confirmation of the conventional model is the He ash experiment.
The modeled helium ash time evolution indicated that the alpha-particle slowing-down calculations and transport assumptions in supershot discharges for the ash are in consistency with the measurements. The best agreement between the modeling and measurements is obtained using the measured radial particle transport and wall recycling coefficients for thermal He. When the slowing-down rate is varied by a factor of 2, the data falls within the expected evolution of the ash density. The time behavior is, however, inconsistent with large irregular energetic alpha particle loss.
The data do not exclude the possibility of modest losses ranging between 20 and 30%. In the highest performance D-T discharges produced on TFTR, the alpha-particle heating is relatively a small fraction of the total power required to heat the plasma, making its detection considerably difficult. Nevertheless, electron temperature rise in TFTR D-T shots during beam injection is greater than in D-only or T-only shots. Recent analysis indicated that the change in electron temperature requires including both alpha heating and isotope effects.
When that database is constrained to take into consideration the change in electron temperature associated with confinement, the residual change has been determined to be in reasonable consistency with the predicted alpha heating. More experiments with a higher ratio of alpha heating to beam heating power will be required in order to calculate the efficiency of alpha heating. 5. Plasma & Space: As it was previously mentioned, during strong solar storms, the Earth’s magnetic field dips a shoulder of ionized gas, or plasma, into the onslaught and sprouts a plasma tail on its backside.
In addition, the planet’s magnetic field splits the sun’s energy into two separate streams. These discoveries, along with much other imagery, are expected to improve space-weather forecasting. These curious features were spotted by NASA’s IMAGE satellite. The magnetic energy that emanates from the planet’s poles and encircles the globe in an invisible protective sheath has been studied thoroughly. The IMAGE (imager for Magnetopause-to-Aurora Global Exploration) satellite was first launched March 25, 2000. The spacecraft follows an egg-shaped orbit that, at its farthest point, captures a whole view of Earth.
The new study is based on ultraviolet light data collected during solar storms that struck the Earth. This so called magnetosphere is the Earth’s front line against space weather. Therefore, scientists want to better understand what goes on when the solar wind strikes the magnetosphere. This interaction is known to push the magnetosphere into a teardrop shape that extends beyond the Moon on Earth’s night side. When the solar wind whips up a strong storm, it can knock out radio communications, disrupt satellites and even threaten power grids on Earth. . 1. Solar Prominences: Sunspots are dark cool areas that appear on the sun’s photosphere, which always appear in pairs and are intense magnetic fields that break through the surface. The field lines leave through one sunspot and re-enter through the other one. This magnetic field is caused by movements of gases in the sun’s interior. It is not really known what causes these sunspots, but two theories have been proposed. Firstly, uneven rotation of the sun might distort and twist magnetic field lines in the interior.
The twisted field lines break through the sun’s surface forming sunspot pairs. Eventually, the field lines break apart and sunspot activity decreases. Secondly, huge tubes of gas circle the sun’s interior at high latitudes and begin to move toward the equator. When they roll against each other, they form spots, and when they reach the equator, they break up and sunspots disappear. Occasionally, clouds of gases from the chromosphere will rise and orient themselves along the magnetic field lines from the sunspot pairs. However, those arches of gases are called prominences.
Prominences can last for two to three months and usually extend 30,000 miles or more above the sun’s surface. When reaching this height, they can erupt for a few minutes to hours and send large amounts of material racing through the corona and outward into space at speeds reaching 1000 km/s forming what is called the coronal mass ejection. The above picture shows a large eruptive solar prominence, with an image of our Earth added for size comparison. However, sometimes in complex sunspot groups, abrupt, violent explosions from the sun occur forming the so-called solar flares.
Solar flares are thought to be caused by sudden magnetic field changes in areas where the sun’s magnetic field is concentrated. Solar flares are associated with the release of gases, electrons, visible light, ultraviolet light and x-rays. These solar flares are the ones responsible for the auroras previously discussed. Some studies, led by the Southwest Research Institute, produced the first global images of this region of space known as Earth’s plasmasphere. It was discovered that during strong solar storms, a buildup of plasma, known as a shoulder, forms on the side of Earth facing the storm.
On Earth’s backside, the plasma is pulled into a long tail that curves out into space and points back toward the sun. The plasma tails were predicted but were very controversial. The tails are thought to form when helium ions near the boundary of the magnetosphere are dragged by the solar wind, but then escape the magnetosphere and are forced by the storm back toward the sun. Studies have also showed that the Earth’s magnetosphere separates the solar wind into two streams of charged particles; protons and electrons. These charges are directed by the Earth’s magnetic field lines.
When these charged particles penetrate to inner portions of the magnetosphere, they interact with the plasmasphere exciting the gases present there. For two decades, researchers have imaged the electron stream, but now the less noticeable proton stream has been discovered. Both streams produce the auroras, though not all of it is the bright and colorful variety seen from the ground. However, it was discovered as well that the proton stream enters the atmosphere at lower latitudes, farther from the magnetic poles, than the electron stream.
This fact is a result of the electrons’ lower momentum. 5. 2. Plasma Rockets: An agreement to collaborate on development of an advanced rocket technology that could cut in half the time required to reach Mars, opening the solar system to human exploration in the next decade, has been signed by NASA’s Johnson Space Center, and MSE Technology Applications Inc. The technology could reduce astronauts’ total exposure to space radiation and lessen time spent in weightlessness, perhaps minimizing bone and muscle mass loss and circulatory changes.
The Variable Specific Impulse Magnetoplasma Rocket (VASIMR) has been under development at Johnson’s Advanced Space Propulsion Laboratory. As we have seen in this paper, plasma is a good electrical conductor, allowing it to be held, guided and accelerated by using proper magnetic fields. The VASIMR engine consists of three linked magnetic cells. The forward cell handles the main injection of propellant gas and its ionization. The central cell acts as an amplifier to further heat the plasma. The aft cell is a magnetic nozzle, which converts the energy of the fluid into directed flow.
Neutral gas is injected at the forward cell and ionized. The resulting plasma is electromagnetically energized in the central cell by ion cyclotron resonance heating. In this process radio waves transfer their energy to the plasma and therefore heat it. After heating, the plasma is magnetically exhausted at the aft cell to provide modulated thrust. The aft cell is a magnetic nozzle, which converts the energy of the plasma into velocity of the jet exhaust, while protecting any nearby structure and ensuring efficient plasma detachment from the magnetic field.
The key to this technology is the ability to vary, or modulate, the plasma exhaust to maintain optimal propulsive efficiency. This feature is like an automobile’s transmission which best uses the power of the engine, either for driving on a level highway or for torque over hilly terrain. However, on a mission to Mars, such rocket would continuously accelerate through the first half of its trip, and then reverse its attitude and slow down through the second half. The flight could slightly take over three months.
Usually, a conventional chemical mission would take seven to eight months and involve in long periods of unpowered drift en routine. Electrical power could be transmitted effectively over long distances with little or no loss of electricity due to having no resistance in power lines, and hence reducing load on power plants’ capacity. For now, the magnets in the lab’s engine draw power from a local electrical utility, but early tests near Earth will use solar arrays. Deep-space tests will likely require nuclear power to provide the wattage needed to heat the plasma. . Conclusion: Throughout this paper, we have discussed this elusive fourth state of matter and its abundance in the universe. Beginning with our sun and its environment, deep beneath its surface, dynamo effects generate tubes of magnetic flux that can bob up and create great arches that become visible as striation of plasma in the solar atmosphere. We have seen how this is mainly the source of the beautiful auroras seen on the poles of our Earth. If we move farther into space, we find that fascinating plasma phenomena continue to proliferate.
The pressure of interstellar plasmas contains the solar wind inside an irregularly shaped region called the heliosphere. Extending for several hundred light years around the heliosphere is a mysterious bubble of very hot, x-ray-emitting plasma that may have been created by a nearby supernova explosion in ancient past. We have also seen that the common source of energy for all of these stars is fusion reactions. When two low-mass nuclei combine together to form a more massive nucleus, this process is accompanied with a tremendous amount of energy.
This sort of chemical processes is the highest energy-releasing reaction of all times. This fact, along with many other ones, such as the availability and low cost of deuterium, have encouraged the scientists all over the globe to try harness the power of a fusion reaction. We have seen that if we want to make fusion a reality on Earth, atoms must be heated to very high temperatures, typically above 10 million K. In this high-temperature state, atoms undergo ionization and form plasma.
In order to get a net energy gain, this plasma must be confined long enough and at high densities for fusion to take place. As a result of these efforts, two methods for simulating what happens on stars here on Earth have been developed; the magnetic confinement of the tokamak, and the inertial confinement. We have seen how the electromagnetic waves, along with Ohmic heating and NBI have all been used in order to heat the plasma in a tokamak for times approaching 1. 4 s. Inertial confinement on the other hand operates on implosions driven by laser or ion beams.
After that, we have discussed how the TFTR experiments on high-temperature plasmas, which culminated in the study of D-T plasmas containing significant populations of alpha particles, spanned over two decades from conception to completion. We have also seen how the TFTR project has contributed to the development of sophisticated diagnostics techniques to study both the background plasma and the resulting energetic fusion products, and computational techniques to both interpret the experimental results and to predict the outcome of these experiments.
Finally, we have discussed some of the promising technologies involving plasma. We have seen how thrust from a plasma engine could boost a spacecraft for a longer period of time and with much better efficiency than conventional engines. One of the plasma engines key features is their capability to throttle, which allows them to increase or decrease in thrust when needed to enter or escape a planet’s gravity.
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