Electric Cosmos: The Solar Capacitor Model. I

Here I'll continue my response to Thunderbolts Forum (TBF) critique of my critique of Don Scott's “The Electric Sky”. In this post, I'll focus on their response to my calculations of the deficiencies of another one of their proposed models for externally powering the Sun.

In this model, presented graphically in figure 1, the sun is powered by radially inbound electrons streaming from the heliopause which acts like a cathode. The photosphere of the Sun acts as the anode for the system, receiving the electrons and converting them to thermal or optical energy by their impacts. The solar photosphere also acts as a source for solar protons and ions as part of the solar wind. The electrons are accelerated inward, and the ions outward by a large potential drop between the heliopause and the solar surface. A first examination of this model resembles the popular spherical capacitor models often examined in the electromagnetism chapters in physics classes, so I will call it the Solar Capacitor model. This model does not have an obvious integration with the larger cosmos, unlike the Solar Resistor model discussed in the previous post, but I'll deal with those issues later.

Figure 1: Components of Electric Sun model

Later in the TBF thread, Don Scott reports a number of values for electrons at the heliopause to explain the solar power source in this model. I'll ignore some of the math errors Dr. Scott seems to make as we're just interested in order-of-magnitude agreement.

* interstellar electron speed of 1e5 m/s
* electron density of 10,000 electrons/m^3

These give an electron current density of 1.6e-10 amp/m^2 which with the heliopause assumed at 100AU (1.49e13 m) places a current across this boundary of 4.5e17 amps. With a voltage drop of 1e9, this yields a power of 4.5e26 watts, a little more than the observed solar luminosity. (Note that we could fiddle with a range of values here to get the same luminosity - 1e10 volts for 4e16 amps would work as well.) We'll use these as our input values to the model. Let's also note that Dr. Scott specifies that the solar wind speed measured by spacecraft runs between 2e5 and 1e6 m/s.

First, I'll outline the basics of the analysis at a level which might be called a first-order approximation - it lays the basic framework while ignoring some of the interactions which would complicate a first analysis. The goal is to get an idea of magnitudes of other quantities we can determine from such a configuration using fundamental physical principles such as energy and charge conservation.

Assumptions:
- radial symmetry. The Sun looks roughly the same regardless of the direction we look at it.
- time independence. We're interested in the bulk steady production of energy, not episodic events like flares and CMEs.
- the motion of electrons & protons are controlled purely by potential at photosphere & heliopause. We can use conservation of energy to determine the particle energy all along the trajectory.

'i' indicated the initial potential and kinetic energy and 'f' index indicates the final potential and kinetic energy values. The kinetic energy of a particle, E_k, is related to the particle velocity by

Here q is the charge of the particle m is the rest mass of the particle, Phi is the electric potential field value at radial position r.
- potential in the space between the Sun and the heliopause is assumed coulombic. This is also a consequence of the radial symmetry of the problem and assumed charge neutrality in the intervening space.

Using this equation, we can solve for the charge necessary to produce a 1e9 volt drop between the heliopause (100AU) and the solar surface (~0.003AU). We see that it requires a net charge a the Sun of +77.44e6 coulombs.

Note that all of the above equations should be familiar to anyone who has taken a competent high-school level physics class.

What are we not including?
- We assume counter-streaming electrons and ions are not interacting. This ignores energy losses due to scattering as well as nuclear processes such as pair production (electron-positrons and muons). All these processes are well-studied in particle accelerators.
- We assume the electromagnetic fields generated by the streaming electrons and ions are small enough to be ignored. Such fields would alter the flows, diverting their energy from going to the solar photosphere.

The advantage of this approximation is that both of the ignored effects described above would reduce the energy of the electrons reaching the solar photosphere by distributing the energy in the intervening space. This means that we get an upper bound, or maximum amount of energy that can possibly reach the solar surface. Inclusions of any of these refined processes will make agreement for the Electric Sun model even worse than we are about to see.

Using the equations above, we can plot the energies, and therefore the velocities of electrons, protons and alpha particles in the region between the photosphere and the heliopause (Figures 2 & 3). The horizontal distance scale is logarithmic for clarity. Note that the Earth is located at 1AU.

The protons and positive ions, repelled by the positive charge of the Sun, are accelerated as they move out. The electrons accelerate on the way towards the Sun.

	Figure 2: Energy of particles vs. radial distance from the Sun. We also plot the potential (voltage) of the solar field. The radial distance is plotted logarithmically in astronomical units (AU).
	Figure 3: Particle radial velocities vs. Radial distance from the Sun. Speeds based on energies from Figure 2. The radial distance is plotted logarithmically in astronomical units (AU).

With a closer examination of the actual values, we see that things start to fall apart for this model very quickly.

* The inbound electrons accelerate to relativistic speeds and are close to the speed-of-light by the time they reach 10AU from the Sun. By the time they reach Earth orbit (1 AU), they have energies of about 4.6 MeV (million electron volts). This is well above the pair-production threshold energy for electrons. Any matter they strike can generate showers of secondary electron-positron pairs. This includes planets, moon, and spacecraft (with and without crews).

* The outbound protons, starting close to the Sun and the strongest gradient in the potential, accelerate to near 1GeV (gigaelectron volts) by 0.1 AU. In velocities, this translates to over 0.87c (=2.6e8 m/s) for protons. Alpha particles (helium nuclei) reach nearly 2 GeV and a speed of 0.75c (2.3e8 m/s). Compare this to the solar wind speed Dr. Scott reports above. The Electric Sun model predicts a solar wind speed that is a factor of over 200 higher than the measured outbound solar wind speed!

Next, let's examine the particle fluxes implied by this model. At the heliopause, an electron current density of 1.6e-10 amp/m^2 corresponds to an electron flux of 1e+9 electrons/m^2/s and a total current through the surface of 4.5e17 amps. Dr. Scott claims that the outbound proton current matches the electron current, keeping the charge density neutral (we'll also see why the charge density will not remain neutral in this configuration), so for this next step, we assume a total number of protons emitted at the Sun is equivalent to 4.5e17 amps. At the photosphere, this corresponds to a proton flux of 4.6e17 protons/m^2/s.

But wait, the charge on the Sun to maintain the billion volt potential drop is only 77.44e6 coulombs! If the outgoing proton flux is 4.5e17 amps, the Sun will lose its entire positive charge in only 77.44e6 coulombs/4.5e17amps = 1.7e-10 seconds! Without an external source maintaining the solar potential, the Electric Sun will shut down in about 170 picoseconds! Remember, we have not yet included the effects of the net charge reduction due to the same amount of incoming electrons! If we include these electrons, the shutdown time for the Sun is even short (i.e. HALF the current estimate).

What maintains this potential?? Where is the incredible power source that maintains it??? That is the REAL mystery of the Electric Cosmos and its advocates never talk about that!

Would you trust an electrical engineer who designed his lighting system (in this case, the Sun) without an EMF to drive it?

In the next post on this model, we'll see even more implications of the Electric Sun model that fail when compared to observations.
(Author's note: realized I had reversed cathode & anode. Fixed 1/4/2009)