This is important for a number of different reasons. As mentioned in the previous post, one important aspect is that the spacecraft needs to survive the radiation environment - an issue far more important in Electric Sun models where all solar energy is generated from particles traveling through interplanetary space. Another issue is that when you design an instrument, say for measuring particle density and/or energy, you need to have an idea of the range of values the detector will encounter and know that it can return valid values, otherwise your ability to interpret the results are limited. Explorer 1, the first satellite orbited by the United States (Wikipedia: Explorer 1 Results), actually encountered the problem where the geiger counter on the spacecraft became saturated from the trapped particle population in the Earth's radiation belts. It actually took a while for the researchers to figure out that the counter was showing no radiation because the radiation was so high it was shorting out the counter.
Revisiting the Solar Cathode Model
Back in the early days of my involvement with the "Electric Universe" phenomenon, I did a very simple analysis of an Electric Sun model based on the description and parameters. One of those models, where the Sun acts as a cathode, powered by electrons accelerated by a hypothesized potential difference between the heliopause and photosphere of billions of volts, were subjected to some basic analysis using fundamental conservation principles. I called this model the "Solar Capacitor" model due to its similarity to spherical capacitors studied in much of the physics literature. EU supporters sometimes call it the solar 'cathode' model and it is based on models originally proposed by Juergens (see References below) and promoted by Don Scott in The Electric Sky. My analyses of this model were summarized in a few blog posts.
My model analysis was the kind of 'back of the envelope' computation that all good scientists and engineers are (hopefully!) trained in to determine if an idea or design might be worth further exploration. In the case of the 'solar capacitor' model, it simply required that electrons from the heliopause had to accelerate sunward under an electric potential that would give them energy sufficient at the solar photosphere to explain the power OUTPUT from the Sun.
In the earlier articles, I mostly focussed on the fact that the fluxes and energies of the interplanetary medium required by electric sun models does not match with in situ measurements. If they were off by a factor of 10 or so, it would be something that might actually be fixable - but the Electric Sun model was off by factors of thousands and more when compared to measurements. This is a pretty reliable indicator of an unworkable theory.
EU supporters, undeterred by these inconvenient facts (particulately funny considering that they claim to regard in situ measurements as the Gold Standard of measurements), construct a variety of excuses to save this model (see Electric Cosmos: The Solar Capacitor Model. III). I cover more of the problems with these excuses in a future article in this series.
The fundamental principles of the model are very basic:
- conservation of particles: no electrons are created or destroyed in the trip from the heliopause to the photosphere, and;
- conservation of energy: an electric potential difference between the heliopause and the photosphere provides the kinetic energy to the electrons on the inbound trip, and to the protons and ions on the outbound trip. I did not consider how this potential difference was formed or maintained.
|Schematic representation of the Solar Capacitor model.|
Computing the Radiation Dose
We'll use the numbers from the earlier analysis for the energy and flux of protons and electrons at Earth's orbit. We start with the claimed inbound electron flux at the heliopause of 1e5 electrons/cm^2/s = 1e9 electrons/m^2/s. We will not use the revised value recently proposed by Dr. Scott (see Electric Universe Fantasies & Heliopause Electrons, Electric Universe Fantasies & Heliopause Electrons. II.) since the value appears to be unrelated to any actual measurements (i.e. made up).
Because the flow of electrons is moving radially towards the Sun at the center, the same number of electrons must pass through each spherical surface centered on the Sun, This means the number of electrons passing through a unit area increases as the electrons get closer to the Sun. It is a spherical converging flow, so at the orbit of Earth, the electron flux is higher by by a factor of the inverse square of the radial position: (100AU/1AU)^2 = 10,000.
With the electrons accelerating through the potential, and gaining energy, we find the energy of the electrons at the orbit of Earth is computed to be 4.6MeV (million electron volts).
Particle Flux: 1.0e+13 /s/m^2 = 1.0e+09/s/cm^2
Mean Particle Energy: 4.6 MeV
This gives a mean energy flux of 4.6e13 MeV/s/m^2
A curie is defined 1 curie = 3.7e10 disintegrations/second, which is the number of decays per second of about one gram of radium 226. (see How the Curie Came to Be by Paul W. Frame). So our electron flux is equivalent to a radioactive source of beta rays with an activity of
(1e13/s/m^2) / (3.7e10 /s/curie) = 270 curies/m^2.
Electrons with energies of 4.6MeV are IONIZING radiation - it can knock electrons out of atoms, turning them into ions and disrupting chemical bonds. Their energy is even well above the pair production threshold to produce matter-antimatter pairs (Wikipedia: Pair Production). This is NASTY stuff if you're exposed to it. The high energy makes it pretty accurate to use the methodologies for computing hard radiation exposure.
Now consider the 'target'. For our example we'll use an adult human being. The area of radiation flux which a human body would intercept can be estimated assuming a human being is about 2 meters tall (6+ feet) and about 0.5 meters wide (about 19 inches). That comes out to about 1 square meter (1 m^2). This might be a little high. Considering the epidemic of obesity in developed countries, this might be small, but most astronauts would not qualify as obese. We'll use this number for ease in computation, knowing that adjusting it will be a simple proportional relationship.
To compute the radiation exposure, we multiply the energy flux by the duration of exposure (we'll use 1 hour =3600 seconds) times the area of the human target (about 1 m^2), and divide it by the mass (about 70 kg = 7e4 gm), since the hazard is how much radiation is absorbed per unit of mass.
To compute the dosage, we must multiply the flux by the area of the target, then divide by the mass of the target in grams:
dosage = flux * area/mass
dosage = (4.6e13 MeV/s/m^2) * (1 m^2) / (7e4 gm) = 6.6e8 MeV/s/gm
To convert to rads, a unit of radiation dosage (Wikipedia), we divide MeV/gm by 62.4e6. We're receiving this dosage each second, so our dosage rate computes to
Exposure Rate: 10.5 rads/s
Since our astronaut is traveling through space, we expect them to at least be exposed for an hour (1 hour = 3600 seconds). So our astronaut's exposure each hour is
(10.5 rads/s) * (3600 s/hr) = 38,000 rads/hr
In the 'solar cathode' electric sun model, radiation exposure at the orbit of Earth is 38,000 rads in one hour!
Compare this to the estimated total dosage for passage through the radiation belts by a spacecraft on the way to the Moon of less than about 13 rads for the entire passage (see Odenwald@SpaceMath, the Deadly Van Allen Belts?). Some of the workers at the Fukushima nuclear disaster (Wikipedia) were exposed to 106 millisieverts = 0.106 sieverts = 10.6 rads (1 rad = 0.01 sieverts).
Above about 300 rads in one hour, you can expect serious health problems, and it gets worse with higher dosage.
If the Sun were actually powered by these currents, we would have a lot of dead astronauts.
At this level of radiation, it is hazardous to robotic spacecraft as well.
Note these were very simple computations, using basic principles of conservation of particles, conservation of energy, and basic geometry. These are the types of 'back-of-the-envelope' calculations that real physicists and engineers often do as a 'sanity check' for ideas.
I'll leave it as an exercise for the reader to complete the dosage calculation for the outward streaming protons. To give you an idea, here's a plot of the dosage rate for electrons and protons computed for this model.
|A plot of the dosage rate by electron and proton radiation with distance (0.1-100AU) for the solar capacitor model. The red vertical line represents the distance of Earth's orbit.|
This is a calculation which can be, and has been, demonstrated by satellite engineers. In the months following Don Scott's presentation at GSFC (Donald Scott, of "The Electric Sky", presents at GSFC), I received some interesting comments from those in the audience who remembered me from that event. While Dr. Scott did not mention Electric Sun models in his talk (a fact that was noted by some members of the colloquium committee) some of them apparently examined Dr. Scott's Electric Sun claims in The Electric Sky and expressed horror at the realization of just how deadly the radiation environment required by the model.
In the next post in this series, I'll go into some of the bizarre excuses EU supporters construct when confronted with this problem.
Update September 10, 2012: Minor edit in references.
- Electric Discharge as the Source of Solar Radiant Energy (Concluded) by Ralph E. Juergens
Kronos Vol VIII.No 2 (Winter 1983)
- eHow: How to calculate Doses from Flux