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Saturday, January 31, 2015

The SPACE for my thoughts.



1. FINDING THE EXTRA DIMENSIONS
Revealing extra dimensions means using small enough "ants", in other words particles whose wavelengths are short enough to "notice" the extra dimensions. That means very high energies, probably even higher than the LHC achieves. But it is possible that the LHC experiments could see some phenomena that indirectly support the existence of these extra dimensions, which would give string theory a major boost.


2. LOOK BACK INTO THE BEGINNING?
When you look at stars and galaxies in the night sky you are looking back in time. The further away an object is, the longer it has taken for its light to reach us. The furthest back we have been able to see is to about 400 million years after the Big Bang. This was about the time the universe had cooled sufficiently for protons and electrons to combine to form hydrogen atoms. Even with the biggest super-telescopes being planned, we will never be able to see right back to the beginning of time for the simple reason that there was no light to see until around 380,000 years after the Big Bang. This is like an optical curtain at the edge of what cosmologists call the Dark Ages, before which there were no stars or galaxies emitting electromagnetic radiation for us to detect.


3. STRINGY DARK MATTER
Another theory states that dark matter may be a higher vibration of the string and we, for example are the lowest vibration (the lowest octave) of tiny little rubber bands vibrating everywhere. But a string can twang and you can have higher vibrations of a rubber band and we think that these higher octaves (vibrations) are dark matter.


4. PATTERNS IN THE DARK
If looked at closely a possible pattern emerges, taken into consideration that these might just be gross approximations, 
1.Having no mass, nor volume - Energy.
2.Having no mass, yet volume - Dark Energy.
3.Having mass, yet no volume - Dark Matter.
4.Having both mass, and volume - Matter.

5. EXTRA DIMENSIONAL DARK MATTER
Have always had the intuitive feeling that dark matter, simply put, is matter from other dimensions in hyperspace. String theory does lead credence to such claims as it supports hyperspace and multi-dimensional particles. Sometimes I fantasize of massive, multi-dimensional galaxies systematically interlaced in between our 3 dimensional space. The laws of EM and optics may be closely related to the fact as to why we can not "see" this matter. Our eyes are the byproduct of evolution. Three dimensional matter produces three dimensional photons aka light and our eyes were designed to see this light. As I write this I realize it may be possible that extra dimensional matter may create extra dimensional light.



6. HIGGS - THE NEW ETHER
This field is made up of Higgs bosons, which would be small particles that bind this field to matter.Sounds a lot like ether to me. In point of fact, if you dig hard enough, it becomes quite evident that what Higgs did was reformulate, rename, or rephrase the ether in a term that was palatable to mainstream physicists; but make no mistake, what he is talking about is ether, plain and simple. This Higgs boson, or binding particle, has also been dubbed the God particle, the particle that gives matter its mass.

7. TACHYONIC IMAGINARY NUMBER 
Gamow tells the reader that, in the 1920’s, in the process of measuring the rate of electron spin, Goudsmit and Uhlenbeck discovered that the rate was 1.37 times the speed of light! Paul Adrian Dirac figured out a way around the problem. As explained by Gamow, Dirac decided to use the imaginary number i, or the square root of negative one to stand for the tachyonic orthorotational speed of the electron. By using this imaginary number, relativity would not be violated. Relativity could now be combined with quantum physics.



8. TESLA’S DYNAMIC THEORY OF GRAVITY – ANYONE ?

Sun was absorbing more energy than it was radiating.
Tesla’s dynamic theory of gravity. All matter is constantly absorbing ether all the time at the tachyonic speed of 1.37 times the speed of light. This is the world of ether. By its nature, the ether exists in a realm that transcends the speed of light. Gravity is simply the absorption of ether by, for instance, the earth. The reason we fall back to the earth when we jump up is not because of some mysterious disconnected force called gravity; we fall back to the earth because we are in the way of the influx of ether. That is what gravity is. It is absorption of ether by the elementary particles. It is the elusive Higgs boson, or God particle, the force/process that gives matter its mass. And it happens in a continuous fashion all the time , the ground state electron is assumed to emit Larmor radiation which causes it to spiral inward, but this does not lead to collapse of the orbit because the electron also absorbs zero-point energy.

9. WIRELESS ELECTRICITY
tesla’s experiments – Unworkable but writable over concepts.

10. WHAT MAKES GRAVITY WEAK ?
Dimensional analysis into the revealing of the forces leaking into the other dimensions. So that the overall effect of Gravity decreases and leads to a inverse squared relationship . Could be explained. 
 
11. PLACNK LENGTH - SIGNIFICANCE
The Planck area, equal to the square of the Planck length, has a clearer role in quantum gravity. Black hole entropy is known to be given by where A is the area of the event horizon. The action in string theory is proportional to the area of the string worldsheet, and area is quantized in loop quantum gravity.


The physical significance of the Planck length, if any, is not yet known. Because the Planck length is the only length that can be formed from the constants c, G, and ħ, dimensional analysis suggests that lengths of special significance in quantum gravity are likely to be small multiples of the Planck length. In some theories or forms of quantum gravity, it is the length scale at which the structure of spacetime becomes dominated by quantum effects, giving it a discrete or foamy structure, but other theories of quantum gravity predict no such effects. If there are large extra dimensions, the measured strength of gravity may be much smaller than its true (small-scale) value. In this case the Planck length would have no physical significance, and quantum gravitational effects would appear at much larger scales.
 
12. GRAVITATIONAL ANALOGY
The trouble with the rubber sheet analogy is that the objects on the sheet don't distort it by themselves. The earth's gravity pulls them down into the sheet. Maybe an expanding balloon in space would be better. The inertia of the objects on its surface would deform it. Maybe objects curve space because they have inertia and the universe is expanding. This theory agrees with the observation that the rate of expansion is increasing. If it weren't we'd have no gravity.

13. GRAVITATIONAL SPEED = C
Is equal to the speed of light that means it must be composed of photon like particles. that left aside when an object does explode does the effect travel of light travel faster or does the gravitational force travel faster.. It would then make sense that effects of gravity only translate through spacetime at c, hence C is the maximum speed to which gravity can accelerate any object.

14. ZERO POINT ENERGY DEVICE(quantum perpetual motion machine)


A thought experiment for a device that readily demonstrates how the Casimir force could be put to use in principle was proposed by physicist Robert Forward in 1984. A ''vacuum fluctuation battery'' could be constructed consisting of stacked conducting plates. Applying the same polarity charge to all the plates would yield a repulsive force between plates, thereby opposing the Casimir force which is acting to push the plates together. Adjusting the electrostatic force so as to permit the Casimir force to dominate will result in adding energy to the electric field between the plates, thereby converting zero-point energy to electric energy.

One can imagine an even simpler microdevice in which the Casimir force pushes two plates together thereby engaging some kind of lever which does work. There is no practical application in these examples since ideally it would take just as much energy, and in practice somewhat more energy owing to frictional and other losses, to separate the plates for a second cycle. Nevertheless, this would demonstrate the concept of conversion of zero-point energy in principle if the Casimir effect attribution to zero-point energy is correct (which is debatable). 

This is owing to the circumstance that the zero-point energy density is assumed to be constant: no matter how much the universe expands it does not become diluted, but instead more zero-point energy is assumed to be created out of nothing.

15. WHY THEORIZE ?
On the other hand don't think that "spin 2" etc will explain much because gravitons are attempts to explain a mathematical result as a physical entity. Sometimes such explanations seem to "explain" things, most of the time we have more math than fits our universe. In other words, even Einstein had some difficulty deciding which mathematical formulation for general relativity would be best to use...he had several and had to discard most......it was the "equivalence principle" which led him to be able to guess which one might match experimental results. "spin two" was an "accidental" discovery hiding within string theory when it was discovered. 

Nobody even knows if gravitons exist, and if they do, where they came from, where they are going, and whether they might survive a grand unification theory (combining quantum mechanics and general relativity). All particles and energy may result from spontaneous symmetry breaking; that's the best theory we seem to have currently. But in fact nobody knows for sure what any particle "is" (Exactly what is an "electron" for instance) maybe a "string"?? Maybe a probability wave function) , nor what time, space, and gravity actually are. What we do have are some neat theories that make predictions and to the extent we can test them experimentally seem to work pretty well. 
It's good to keep in mind things (the world around us) are very deceiving: are you the "same" person you were a year or two ago?? Not really, just about every cell in your body has been replaced!!! Our five senses are narrowband filters that keep out 99.9% of what is around us so we are easily mislead. Somehow, though, our brain has developed beyond our meager senses. So we are able contemplate "gravitons" even though we cannot sense them.



16. EM SPECTRUM’S EXTENSIONS 
The long wavelength limit is the size of the universe itself, while it is thought that the short wavelength limit is in the vicinity of the Planck length, although in principle the spectrum is infinite and continuous. 

17. DISTURBING THOUGHTS

Oscillating universe theory
Q: 1 So if the universe keeps oscillating like bang-crunch-bang again. What could the purpose be?
Ans: to find as many possibilities for the created to find out about The creator . Its the ultimate satisfaction a creator can get. when his creations are able to figure out and understand the creator himself . Maybe thats the ultimate purpose of the created. to figure out who's the creator. 


Q: 2 If we are created by chances , was it to enjoy life as a gift and be done with it and thats all ?
or has it been given to seek the ultimate truth ? is there an ultimate truth.
Or is like the lies we use when we need to please someone ?
Possible Ans : If everything is an accident, there's no reason to figure anything out. If everything is futile, purpose is an imaginary concept. But if everything was created, and if everything has a purpose, shouldn't it be the underlying goal of all mankind to discover that Creator and find that purpose?  And so we endeavor to discover our Creator and fulfill our purpose, while using science as merely one of our tools.  So we should include the speculation that God may have created everything for a purpose and that perhaps the universe we see is evidence for God.



18. MATHEMATICS OF LOGIC.


a.) Gödel's first incompleteness theorem states that: Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory


b.) Gödel's second incompleteness theorem can be stated as follows:
For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.



The math behind discovering everything that does and even all that does not!

To start with an idea that would seem like a summation of all human knowledge in one single paragraph of understanding, a few assumptions have to be made. At any point if you feel uncomfortable with accepting these assumptions you can feel free to carry on or drop out. 

Assumption 1. There is a finite extent of the universe till which we can probe details into, using the information that has originated from the big-bang and how far it has travelled it has travelled in that time since it originated.

Assumption 2. There is an extent of the universe which is beyond our probing and assimilation, within which (if finite) exists possibilities that cannot be understood by the laws that describe our extent of the universe.

Assumption 3. Within this domain that is unavailable to our grasp, exists every possibility of circumstance and environment. Hence every event that can happen (can be imagined or cannot be imagined) within this domain has  a finite infinitesimal probability of occurring. All the events that cannot occur also have a infinitesimal probability of happening (say P(E)= 1E-50), the probability being so low that it tends to zero(but still isn't zero) in our universal scales.

Suppose you have an engine which runs Assumptions 1 to 3 constantly for an indefinite period, entering the finite region to a domain beyond our reach, it will eventually churn out the entirety of events that can ever be known for the history of time, because of the fact that even if something that had the probability of an event occurring in assumption 3, this machine would make a certainty, It would occur!

The Curious Case of Magnetic Confinement Fusion

An uncomplicated & compact comparison of TOKAMAKS and STELLARATORS features, to determine their relevance in attaining the goal of Magnetic Confinement Fusion.  Pranay Valson  

The General Fusion concept: Magnetic Confinement

Starting right at the basics when we assume a general understanding of magnetic confinement fusion (MCF) we are aware of two main devices tokamaks and Stellarators. Both the devices have certain attributes that make them alike and then certain other features that completely differentiate them. There are historical reasons as to why of the two devices the one leading in research for achieving ignition is the tokamak and why the stellarator remains behind in the direction of the same developments. This will also culminate in the global effort on the International Thermonuclear Experimental Reactor which is essentially a tokamak with a configuration and design based on previously unsuccessful (in reaching ignition) designs but just bigger In size (in plasma physics size matters, we shall shortly see how). But before we know why Tokamaks have the lead and also funded with greater enthusiasm in general.
International Thermonuclear Experimental Reactor (components)
It is important to understand the mechanism behind magnetic confinement fusion (MCF) and the specific aspects within it that lead to the main difference between the two machines. For fusion, It is obligatory that light hydrogenic (or isotopes) atoms are stripped of their electrons to enable the nucleus to collide with another such species of ion. This is a binary collision occurring between the two ionic species (they may be same or different) and a plasma consists of these entities maintaining overall global neutrality. In order to overcome the coulomb force of repulsion between the positively charged particles so that the force of repulsion may be overcome by the strong nuclear force of attraction, leading to the two nuclei coming together to form a new nuclear species, this reaction has a certain mass defect from which energy is attained from the whole reaction. The energy attained is proportional to the square of the mass deficit times the speed of light (pure mass to energy conversion). However we need to gather sufficient kinetic energy in the ions motion to be able to even be close to overcoming the columbic force of repulsion and once we bring them together the probability that they come together to fuse should be high , this is often referred to as the collisions cross sections. The higher the cross section ,the higher the probability.

D-T nuclear reaction and Collision Cross Sections
Helical Trapping of charged particles
Different confinement systems are able to do this in different ways. Gravity is one such confinement type which is the source of the kinetic pressure for ions to fuse with each other, on the stars such as the Sun. On earth however we do not have this resource at our disposal considering we do not know specifically know how to manipulate the force of gravity, since it is not very well understood nor completely assimilated within the scope of our current explanatory theories of which quantum mechanics dominates (however if we were to understand this , It would give us more possibilities for exploring fusion). Assuming, that all this is occurring in vacuum so that the ions don't actually collide with species that we do not desire nor think as possibilities in attaining fusion. One possible system is Magnetic confinement Fusion, It is well known the charged particles such as ions undergo a process of entrapment or motion along lines of a magnetic field. This can be explained by the Lorenz force in which a charged particle having a velocity along a given direction is in the presence of a magnetic field ("lines of force"), and not moving along the direction of the magnetic field undergoes gyro motion . 


                                         
This is action of the magnetic force on a charged particle due to the force of electromagnetism. Note that the action due to magnetic field is a cross product hence the revolution around the flux lines. But the revolution has a centre which drifts along a electric field. This is due to the nature of action of the electric field on the charged particle itself. This component of the force causing revolutionary motion on the charged particle, combines with the drift in it centre leading to helical motion around the fixed lines of flux. Depending on the charge on the species ions or electrons the helical motion is in opposite directions.

It is obvious that neutral species need to be ionized in order to be confined by this mechanism otherwise they will escape. In case of naturally occurring gases they can be ionized by applying a very high voltage thus stripping the electrons from the atom's nucleic force of attraction and freeing the atoms of their electrons making them ions. So now in place of randomly moving ions we have confined them to magnetic lines of force. 

The Tokamak ingenuity: The First Attempt


It is required the now trapped ions do not escape our magnetic bottle containing the fields. The easiest way to avoid doing this is by converting the bottle into a torus, in which the ends meet up. But this leads to the complication that the field lines are no longer straight. Due to this there is a drift vertically across the field line on the charged species. This is true for any magnetic fusion machine with a toroidal configuration.
The Rotational transform for Tokamaks

There would follow a charge separation due to this motion across the field lines and hence neutrality would be destroyed and confinement will be lost. This is bad for fusion, since we need charged particles to be moving towards each other and not drifting apart across the field lines. The way to resolve this is by an additional magnetic field in a poloidal direction. In the case of confined plasma in a vacuum sealed container the toroidal field as we saw could be provided simply by loops of currents running around the poloidal cross section throughout the torus. It was the Russians Igor Tamm and Andrei Sakharov in about 1950 ,[E A Azizov 2012 Phys.-Usp. 55 190] who realized that the additional poloidal field which could solve the problem of drift and charge separation could be generated by the plasma itself by inducing a plasma current in it, the plasma itself being a good conductor. At that point in time with geometrical symmetry a necessity this was an ingenious solution. The combination of the poloidal and toroidal fields leads to a net field which is called the rotational transform; this makes the charges species gyrate from the top of the toroid to the bottom hence preventing a vertical charge separation. Another important aspect to this is that the field lines should close in on themselves. The number of times they need to go around the torus in order to do that is called the toroidal number m. The number of times they revolve around the radius of the torus before closing in on themselves is the poloidal number n.                                                
The nested field lines going around the torus form surface in through the torus and it is essential that the field lines lie on this surface; this is called the flux surface. Along a given flux surface with constraints of geometric symmetry it can be expected that the properties of the plasma such as its temperature density etc. remain the same approximately.  The flux surface almost guarantees perfect motion of the charges species along the flux surface and hence giving additional control to its movement. This is the case in which the charged species would not collide with one another. This is crucial for confinement. However not all plasmas are collisionless, this brings in additional complication.

 Inescapable Faults: The Toroidal Plasma Current


 Nested Flux Surfaces in a tokamak
For tokamaks each Toroidal Field coil (which produces the toroidal field) added to increases in costs. Though a maximum number of them are required to generate the toroidal field and reduce the ripple due to the spacing between the coils. It has been found that transport of the impurities in the plasma is higher for higher ripple hence it is advantageous to reduce ripple, [Allen H .Boozer, J. Narl Davidson 1976 Nucl. Fusion 16 731] More the number of coils, lesser the space to occupy for diagnostics that get the plasma properties (without which it is akin to running a machine in the dark). The case of increasing costs of construction then becomes a very tangible reason in a real world scenario. It has been found that certain configurations (not perfectly circular) but D shaped plasmas are optimum for tokamak operation and control. [E. A. Lazarus et al. Phys. Rev. Lett. 77, 2714 ] This puts additional constrains on the geometry of the devices and the space available at the centre for diagnostics and repair of the main transformer primary in case of a failure. 
The soviets from their ingenuity as we saw before decided to use to plasma in order to generate the poloidal field to obtain the rotational transform. They did this by inducing the current in the plasma, using a winding along the centre of the torus which ran a current in the primary winding. Depending upon how much current is run through the plasma.  The resulting rotational transform would be tweaked. However the various instabilities in plasmas were the lesser known evil in those times. Hence there is incomplete control since plasmas under different conditions can behave in different ways. The case of sudden loss in all confinement due to these instability such as 'kink modes' ,  'saw teeth' and 'resistive' , 'neo classical tearing' modes limit performance in the plasma leading to a complete loss of stored energy in the plasma [R.J. La Haye et al 1997 Nucl. Fusion 37 397]. These can cause severe damages to plasma facing components present on the inner sides of the tokamak. It is in principle possible to develop disruption mitigation techniques which follow a method current tailoring which then affects the rotational transform profile.  Magnetohydrodynamic (MHD) stability is low in these cases nevertheless. The density in tokamaks is also limited by the greenwald density limit because of destabilization of magnetic islands by radiation losses. [Gates D A and Delgado-Aparicio, L 2012 Phys. Rev. Lett.108 165004] . The plasma current is proportional to the time rate of change of the solenoid current transformer primary. This leads to a shot like operation in which the current is increased from a negative value to a large positive value. Of course running several Tokamaks in a shot like operation could be a solution but these further increases costs and is highly impractical. The mechanical and thermal stresses generated on the structural component due to this shot like operation is also a real case for structural failure. All the while this requires higher investments in steels and superior components manufacturing technology to reinforce their strengths. For the small times scales of operation and to provide feedback for current tailoring is an engineering challenge that has yet to be met or put into operation. For these additional coils are required around the tokamak further increasing the already rising costs of the engineering excellent plasma facing components and diagnostics and coils.  It seems to be the case of additional complexities in the face of existing problems, thus a revamp in the whole idea would be required to face the adding complexities.

The Stellarator Solution: The Rotational Transform


The primary difference between the Stellerators and tokamaks in understood within the domain of the rotational transform. Stellarators have a design, in which there is no such dependence on the plasma for the rotational transform, and it is not needed to induce a plasma current for the generation of the rotational transform, this makes them a serious candidate for a fusion machine besides the existing tokamak (lacking this feature). The Insight for the development has been granted to Lyman Spitzer of Princeton Plasma physics lab, he individually came up with concept of a stellarators .[Lyman Spitzer Jr ,Phys. Fluids 1, 253 (1958);]  Further Spitzer and mercier proved mathematically that there are there ways of producing a rotational transform of a toroidal magnetic field. They expanded Maxwell's equations in the presences of a magnetic field; the expression for the average no of poloidal turns of a field line in one revolution calculated by them can be shown as below. There are three main ways of twisting the magnetic field

1. Driving the toroidal current, this allows the machine to be axisymmetric making it easier build but like seen before it is non-steady state, already existing tokamaks.
2. Elongating the flux surfaces and making theme such as the LHD device in Japan.
3. Making the magnetic axis non planar, so that τ0 flux surfaces are not guaranteed and they need to be generated by finely engineered coils down to the mm. Making it non-axisymmetric and in many cases such as the TJ-II.  [P Helander et al .Plasma Phys. Control. Fusion 54 (2012) 124009]

J is the current density on the magnetic axis, N is the interger of topological origin eη = r2/rthe elongation of flux surface, d(l)  the tilting angle with respect to the curvature vector K = db/dl where b = B/B is the unit vector  along the magnetic field B. and τ denotes the torsion shown in the figure  
Rotational Transform in a Stellarator
The entire rotational transform is generated by specifically designed and constructed coils; conductors of the toroidal machine, thus giving something close to complete control on the motion of charged particles on the flux surfaces and the rotational transform itself. In the following study we shall see why it is a better idea to use the latter in place of the former in light of the various different phenomena that have been discovered in recent times that makes the operation of Tokamaks detrimental to the magnetic confinement fusion programme.

Future Reactors: Steady State Machines


Flux Surfaces and Coils in the W7-X

Stellarators would easily avoid all these problems simply by specifying the entire rotational transform on its own magnetic coil configuration. The realization that many of the problems tokamaks face can simply be overcome, not by tending to techniques to reduce or address those inherent problems but rather by making complex coils geometries is the key towards a future reactor.  The analysis was of course numerical to be more precise and hence it took larger time for
the concept to be accepted in the MCF community as a viable solution to the above problems. The Russians again experimentally determined, by using helically twisted coils around a toroidal chamber and additional poloidal coils that it was indeed possible to run a continuous discharge without the necessity for plasma current. Without the need for the plasma current, activities could now be focused entirely on the plasma shaping and heating which if sustained well would lead to the steady state operation machines envisioned for reactor scales. Instabilities such as kink modes, saw teeth and resistive, neo classical tearing modes are absent making it disruption free. The toroidal current is however not completely eliminated; stellarators have a bootstrap current (in low collision mode) and Pfirch –Schulter currents parallel to the magnetic field since the perpendicular current is not divergence free. However the magnitude of this current is substantially smaller than compared to tokamaks. It is possible to contain neo-classical tearing modes that may arrive from such currents. Stellarators unlike tokamaks do not experience the plasma terminating disruptions, [Yamada H 2012 private communication]. In stellarators the plasma density is also not limited by greenwald density [Greenwald M 2002 Plasma Phys. Control. Fusion 44 R27] but rather by how radiation Is lost form the plasma core. This hence depends on the concentration and the loss of impurities. But because of this they can operate at higher densities compared to tokamaks. The primary problems of disruptions is completely eliminated, however due to the lack of toroidal symmetry additional problems arrive such as the "ripple" transport. Numerical calculations can make sure the flux lines are closed however; transport losses such as this contribute to a decrease in confinement. The problems of ripple transport were overcome by a physicist named Allen Boozer.  [Allen H .Boozer, J. Narl Davidson 1976 Nucl. Fusion 16 731]

The challenge in Stellarator development is to design the outer flux surface (OFS). At the max-Planck institute it was understood that the last outer flux surface could be enclosed by an overall twisted toroidal surface.  This outer twisted toroidal surface could be generated using specifically twisted or fringed conductor coils placed next to each other giving rise to the overall stellarator field configuration. An remarkable example of this is W7-X at IPP Greifswald, one of the largest stellarators of its type which uses superconducting coils to generate a very high magnetic field. The accuracy in engineering of the coils however it of tantamount importance due to the necessity of the perfect last closed flux surface (as the rotational depends on this absolutely and wholly). However the design also has some additional advantages since the coils are individually constructed, any problems in one of the coils could be easily resolved by removing this and replacing it immediately to resume activities on the machine. The higher aspect ratio, of the stellarators also provides for greater space in the inner circle of the High B field side. thus increasing access and allowing placement of diagnostics and heating devices for the plasma in this space. The number of configurations thus for a stellarators is immense considering the machine can be tweaked in design for improving and optimizing the aspect ratio, cross sectional shape, current or magnetic field strength. The method chosen by the VMEC code can resolve this issue [Hirshman S P, van Rij W I and Merkel P 1986 Comput. Phys. Commun. 43 143], this code makes sure of the existence of the nested flux surfaces.

It is a crucial aspect in stellarators that alpha particle pressure  Pαs~Te3/4/ne is proportional to slowing down time, this is smaller than compared to tokamaks, credited to the ability of the Stellerator to operative above the greenwald limits. We are also aware that fusion power Pfus ~ n­e2Ti2,  the alpha particle pressure scales as pα ~ ne-5/2,therefore increasing the density brings down the alpha particle pressure which is great to reduce the losses due to impurity transport and radiation. The advantages are very clear making it a steady state, high density, disruption free continuous machine but with complex geometry. However the existence of unconfined particle orbits such as those for alpha particles can lead to high neoclassical transport of the thermal particle species.  The effective diffusivity scales as the following De~ eeff3/2Te7/2/ neB2R2
 Collisionality Regimes for Tokamaks and Stellarators
Here eeff is the quantity that symbolizes confinement quality, vd is the drift velocity , Te is the electron temperature and R is the major radius of the device. Due to higher Te scaling, neoclassical losses are higher at high electron temperatures. The transport regions on the outer edge are attributed to turbulence losses. The so-called ‘mono-energetic’ diffusion coefficient versus collisionality, ν = νR/ιv, where ν is the mono-energetic pitch-angle-scattering frequency, R is the major radius and v is the speed of the particles.
Stellarators as we have seen have neoclassical transport due to fiction between the bulk ions and impurities  and this is high, this is due to the 1/ν regime, therefore transport of particles dominates almost the entire plasma volume. The magnitude of this transport can be reduced significantly. It is predicted that these problems can be easily resolved by making the field approximately quasi-isodynamic, so that the thermodiffusion and the radial electric field is small.  

Conclusions: A Stellarator Bias

Triple Product Vs Functional time for Fusion Devices

Hence we have seen that tokamaks with its inherent problems may be able to achieve ignition with the ITER, but it will not be able to sustain this for longer periods due to its pulsed operation. DEMO which is the fusion reactor will have features from ITER but will be flexible to accommodate results from Stellarators like W7-X and future devices this is crucial for the long term goals of achieving steady state working conditions. Though difficult to construct and build, stellarators will be engineered with better facilities to account for the preciseness required. The flexibility that it provides allows for the development of various configurations depending on the conditions for operation.  The performance limited only by neoclassical transport but this also possibly remedied by field optimized stellarators for operation at high densities. It would be wise to wait for the results of W7-X before continuing work on the ITER since, H mode plasmas have also been demonstrated for Stellarators like W7-AS with edge localized modes and may bring new concepts to the table for DEMO. Although the projected performance of W7-X is an order of magnitude lower than that of ITER, results would be available sooner and would go a long way to give further understanding of the machines capabilities towards contributing for the DEMO.