Asymmetric Capacitors

NASA published the paper Asymmetrical Capacitors for Propulsion by Canning et al. and the American Institute of Physics published High Efficiency Lifter Based on the Biefeld-Brown Effect by Einat and Kalderon.

The ions fly towards the small conductor and overshoot. The ions are accelerated in the space between the two electrodes. This creates a momentum distribution of fast moving particles distributing momentum over a large area. The larger ions move in the opposite direction creating low pressure above the lifter and high pressure below the lifter.

For every action there is an equal and opposite reaction.

Asymmetric Capacitors and Propulsion

NASA published the paper Asymmetrical Capacitors for Propulsion by Canning et al. and the American Institute of Physics published High Efficiency Lifter Based on the Biefeld-Brown Effect by Einat and Kalderon.

These lifters or pressers push a mass from the big end of an asymmetrical capacitor to the thin end. The big end of the capacitor becomes a source for electrons. These electrons accelerate and move past the positive small end of the capacitor at a fast speed. For every action there is an equal and opposite reaction.

The space between the electrodes in the asymmetrical capacitor accelerates the electrons. A slow wind moves from the small electrode to the big electrode. More pressure is found underneath the lifter when it is lifting.

Electricity and Return Current

Universal to the concept of electricity is the idea of a return current. No circuit can exist without the return. Electrons under pressure will tend to pop, one at a time, towards an area with less electron pressure or negative potential voltage. In this case the return current may not be a discrete electron returning to where the original kinetic electron left. Instead, a number of electrons will drift in to back-fill where the kinetic electron left.

The electrons will leave according to the probability mass function lambda to the k multiplied by e to the negative lambda divided by k factorial where lambda is the electron ejection rate. The Poisson distribution tells us that for a certain period of time and a certain surface area an average ejection rate will be described by the equation described above. 

The flux in the flow of electrons as energetic electrons move one way and then less energetic electrons back-fill in large numbers moving in the other direction show the capacitive charging of a dielectric medium. Electron kinetic energy begins to move both ways as the medium maximizes the energy stored in the kinetic electrons in the medium.

Electron Movement at a PN Junction

Electrons must move faster at a pn junction. The root mean squared speed of electrons must increase as they move from one side to the other side of the junction. There must be a pressure exerted by a static voltage. This pressure must be described by a statistical process.

Electrons entering the p end of the pn junction with extra energy sit on the edge of the junction and become part of the pressure process. This is the reverse bias case. Electrons entering the n side of the pn junction with extra energy are conducted through the depletion region to the p side where they are conducted out of the diode.

Electron Movement in a Capacitive Structure

So just how do electrons move. We know that they move very quickly. Electrons move at a fraction of the speed of light. These electrons tend to move around a more massive nucleus and can be fit into orbitals. Various levels of energy can be attributed to these orbitals.

Do electrons move differently when they are in the presence of a capacitor, inductor or resistor? This blog post seeks to explore the statistical process of electron movement in the presence of a capacitor. Perhaps in capacitors electrons move as the pistons move in a boxer engine.

We know that charge carriers pile into capacitors as the voltage increases. An uncharged capacitor contains no potential energy. When the capacitor is charged we say that the electric field formed charging the capacitors contains energy. But what does this look like from an electron movement point of view. How far are electrons traveling and if they travel far why doesn't electric current just flow?

When a coulomb of electrons approaches a capacitor some charge makes its way through the capacitor and out the other end. This is not like a conductor though. As the charge makes its way through the dielectric the charge is replaced by electrons bonded to the dielectric. These bonded electrons are far less energetic than the electrons they are replacing.

Electrons flow into the dielectric and are replaced by less energetic electrons until all of the charges match and the capacitor is said to be charged. Back to the analogy of the boxer engine where we have pistons and electrons moving one way and almost at the same time we have a counter movement of electrons or pistons moving in the opposite direction. All of this happens at a fraction of the speed of light that is to say very quickly.

The Maxwell-Heaviside Equations

This blog has been alive for two years and I wanted to reflect on the basic tenants of electromagnetics. Namely, the four Maxwell-Heaviside equations. These four equations and the Lorentz force equation backbone electromagnetics for all practicing electrical engineers.

Gauss' law of electricity is useful as it shows the direction that a  charge will travel in given the presence of an electric field. The electric field is a useful construct because its magnitude gives us insight into the behaviour of electric phenomena.

Gauss' law of magnetism is somewhat less useful. A magnetic field is the normal vector in the curl of an electron field. Gauss' law of magnetism points out that the divergence of a curl is zero. That is the magnetic field is electrons curling and the divergence of that curling field is zero. This fact is also a vector calculus identity.

The Maxwell-Ampere equation can be read two ways. The curl in a magnetic field gives a current and the curl of electrons gives a magnetic field which is the normal to the field of curling electrons. The curl of a curling field does add up to a current. This is backwards from the way we should be thinking about electricity. The current in a wire generates a magnetic field which surrounds the wire. The current from the wire spins off a type of leakage current which spins. The telegraphers equations dictate this type of behaviour.

The Maxwell-Faraday equation involves Lenz's law and the principle of electromagnetic induction. The equation, in differential form, states that the change in a magnetic field will be a curl in the electric field. Understanding what is really going on takes closer consideration. When a loop of current sees an increase in the curl of an electron field one has to consider the nature of the curl. The curl in the electron field is very tight as it was generated by a permanent or electromagnet. The magnetic domains or curl in the electron field of the coil is random.

Due to particle interactions the coil starts to see a tight curl in its electron fields. The law of conservation of angular momentum causes a Lenz' phenomenon curling in the opposite direction. This phenomenon is harnessed as current to drive a load in an electric generator.

When the Maxwell-Heaviside equations were developed the developers had jar batteries, wires and coils at their disposal. Reconciling their world with a modern electronic world takes understanding and patience.

On Capacitance

How capacitance works is poorly defined. Some texts will point out that a dielectric is polarized such that energy is stored to counter the prevailing electric field. But what are the electrons doing? How are these electrons moving? I have explored this topic previously and will revisit it again because capacitance is complicated and so many texts make it sound simple.

The energy in a capacitor is proportional to the voltage squared. Voltage is the excited energy of an electron. Energy is also proportional to the dielectric constant of the dielectric material. The surface area is also proportional to the energy stored but the surface area is not always equal on both plates of a capacitor but we will get to some of the subtleties of capacitance later. Lastly, the energy stored between two plates of a capacitor is inversely proportional to the distance between the two plates or poles.

So what are the electrons doing in a capacitor to store energy? First they move. Electrons move at a fraction of the speed of light. Estimates of how fast an electron move vary but electrons don't move at the speed of light. Electrons don't move at speeds a regular person could understand. Electrons move at a fraction of the speed of light that is to say a speed that is meaningless in kilometers per hour.

We know that electron take in a large number of electrons before they begin to excite at the voltage levels of the conductor charging the capacitor. Electrons flow in and the voltage or excitement of the electrons in the conductor don't immediately rise. The electrons flow through the dielectric to the return and are immediately back-filled by electrons in the dielectric. As more energized or higher voltage electrons enter the dielectric the dielectric becomes more energetic. The electrons that are back-filling the incoming electrons have a higher and higher voltage until their voltage matches the incoming electrons. The capacitor is fully charged.

When a capacitor is fully charged there is an excitement at both plates. The capacitor has a lot of statistical properties that may well have to do with the exponential distribution or the Poisson distribution. Electrons will move into the dielectric with a high relative energy and they will keep moving towards the return. Eventually the electron will return towards the energized plate. It is the continuous dance between the energetic plate and the return that constitutes capacitance. Electrons moving quickly towards the opposing plate only to be back-filled by electrons seeming to polarize the dielectric.

The statistics of electrons in a capacitor has yet to be fully understood. Understanding that things are not fully understood is the first step in understanding the capacitor and eventually the diode and transistor.