CALC-013

Where the beam heats the ionosphere, and by how much

Question this answers. If plasma heating is significant at SBSP beam intensities, how much energy does it actually take, and where does it go? The two halves of the answer point opposite ways, which is the interesting part.

The absorption calculation

Non-deviative absorption, the standard collisional form:

kappa = (e^2 / (2 eps0 me c)) x Ne nu / (omega^2 + nu^2)     [1/m]

  Ne   electron density, m^-3
  nu   electron-neutral collision frequency, 1/s
  omega  2 pi f, wave angular frequency

Evaluated over a three-layer slab at vertical incidence:

Two checks. The frequency ratio is 9.184e-06 / 1.639e-06 = 5.60, against the inverse-square expectation of (5.8/2.45)^2 = 5.60. And SRC-105 independently computes 29.4 kW at 2.45 GHz and 5.11 kW at 5.8 GHz from a 1 GW beam, a fractional loss of 2.9e-5: the same order as this estimate, about three times larger, and its own ratio of 29.4/5.11 = 5.75 is close to 5.60. A three-layer slab sitting a factor of three below a full-path calculation is the expected direction and size of error.

Why a negligible loss still produces a measurable effect

This is the part worth keeping. The absorbed energy is a rounding error, but the electron gas has almost no heat capacity to absorb it into.

D region, ~90 km:
  electron thermal energy density   = 4.142e-12 J/m3
  volumetric heating from the beam  = 5.152e-09 W/m3
  time to double electron temperature = 0.80 ms      (ignoring all cooling)

So the beam loses nothing worth counting and perturbs the medium substantially. Equilibrium is set by heating against collisional cooling, which is exactly the balance the 1978 energy equation solves. This is why every consequence found on QST-009 is a propagation or interference effect and never an energy one, and it is the direct reason the efficiency line closed as it did (CLM-0100): the 1978 efficiency chain has no ionospheric term because there is nothing to put in it.

Limits

Representative layer values rather than modelled profiles, and vertical incidence. The absolute figure should be quoted from SRC-105, not from here. What this calculation establishes on its own is the order of magnitude, the frequency scaling, and the heat-capacity argument.

CALC-013 ADDENDUM, 2026-09-03: the framing was wrong, and the evidence was already held

The calculation stands. The sentence built on it did not.

CALC-013 concluded that the ionosphere "loses nothing worth counting", and CLM-0100 hardened that into "a phase problem, not a loss problem". That holds only for a quiet ionosphere.

SRC-104, the 2004 ESA review, computes the same integral at 2.48 GHz and reports:

A loss of just over 20 per cent during a severe geomagnetic storm, at essentially the SPS frequency, from measured density input. Four orders of magnitude above the quiet case.

The quiet-condition figures never actually disagreed

"Over 99.7 per cent remains" is a bound, not a point estimate. Both finer figures satisfy it. There is no hundred-fold conflict between the sources in quiet conditions; the large variation is between CONDITIONS, and reading a bound as a measurement invented a disagreement that is not there.

What this cost, recorded

CLM-0107 recorded my judgement that about 10 per cent loss at 2.45 GHz was implausible, reasoning from the f^-2 scaling. The reasoning was sound and the conclusion was wrong, because the input that changes is not frequency but the density-collision product, and a CME moves it far enough.

The disconfirming figure was on page 8 of a document held since the earliest ingest and cited in several claims. The failure was not accepting a second-hand summary or misreading a source. It was asserting an implausibility from a scaling argument without first searching the sources already held for the quantity in question. That is a cheaper check than the one I did instead.

Superseded by CLM-0108, CLM-0109 and CLM-0110.

Cite this