From a92698ccb7e22235aa06eb5357bbc489a53fcfa9 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Fri, 22 Mar 2024 00:32:05 +0000 Subject: [PATCH] build based on 27c46ea --- dev/.documenter-siteinfo.json | 2 +- dev/generated/basic/index.html | 6 +- dev/generated/basic_homogeneousamplitude.png | Bin 20852 -> 20790 bytes dev/generated/basic_homogeneousphase.png | Bin 21859 -> 21824 bytes dev/generated/basic_segmentedamplitude.png | Bin 20962 -> 20970 bytes dev/generated/basic_segmentedphase.png | Bin 22304 -> 22198 bytes dev/generated/ground/index.html | 2 +- dev/generated/ground_day.png | Bin 59467 -> 59543 bytes dev/generated/ground_night.png | Bin 71909 -> 71942 bytes dev/generated/integratedreflection/index.html | 2 +- .../integratedreflection_difference.png | Bin 22724 -> 22841 bytes dev/generated/integratedreflection_time.png | Bin 19707 -> 19721 bytes .../interpolatingfunctions/index.html | 10 +-- dev/generated/interpolatingfunctions_amp.png | Bin 51073 -> 51437 bytes .../interpolatingfunctions_phase.png | Bin 43520 -> 45440 bytes dev/generated/interpreting_betas.png | Bin 52805 -> 52907 bytes dev/generated/interpreting_collisionday.png | Bin 44686 -> 44638 bytes dev/generated/interpreting_collisionnight.png | Bin 48824 -> 48867 bytes dev/generated/interpreting_frequencies.png | Bin 62825 -> 62758 bytes dev/generated/interpreting_hprimes.png | Bin 44154 -> 44191 bytes dev/generated/interpretinghpbeta/index.html | 2 +- dev/generated/io/index.html | 4 +- dev/generated/magneticfield/index.html | 2 +- .../magneticfield_daytime_amplitude.png | Bin 32089 -> 32058 bytes dev/generated/meshgrid/index.html | 8 +-- dev/generated/meshgrid2/index.html | 4 +- dev/generated/meshgrid2_20knightfinemesh.png | Bin 218417 -> 218120 bytes .../meshgrid2_20knightfinemeshzoom.png | Bin 224785 -> 224824 bytes dev/generated/meshgrid2_20knightmesh.png | Bin 342520 -> 342600 bytes dev/generated/meshgrid_100kdaymesh.png | Bin 292784 -> 292660 bytes dev/generated/meshgrid_10kdaymesh.png | Bin 309087 -> 308893 bytes dev/generated/meshgrid_20kdaymesh.png | Bin 346136 -> 346502 bytes dev/generated/meshgrid_20knightmesh.png | Bin 345647 -> 346083 bytes dev/generated/multiplespecies/index.html | 2 +- dev/generated/multiplespecies_amplitude.png | Bin 34151 -> 34196 bytes dev/generated/wavefieldintegration/index.html | 18 +++--- dev/index.html | 2 +- dev/lib/internals/index.html | 58 +++++++++--------- dev/lib/public/index.html | 12 ++-- dev/references/index.html | 2 +- 40 files changed, 68 insertions(+), 68 deletions(-) diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 2488bdf..71da811 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-03-16T05:42:13","documenter_version":"1.3.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-03-22T00:31:52","documenter_version":"1.3.0"}} \ No newline at end of file diff --git a/dev/generated/basic/index.html b/dev/generated/basic/index.html index ff76cf7..fa6726f 100644 --- a/dev/generated/basic/index.html +++ b/dev/generated/basic/index.html @@ -21,7 +21,7 @@ rx = GroundSampler(distance, field)
GroundSampler{Float64}(2.0e6, LongwaveModePropagator.Fields.Ez)

Finally there is a Receiver struct which is defined with a geographic location and Antenna, but it is not exported because geographic information is not currently handled by the package.

Waveguides

The abstract LongwaveModePropagator.Waveguide type is used to describe the earth-ionosphere waveguide with a BField, Species, and Ground.

The basic concrete waveguide type is a HomogeneousWaveguide, with fields

If not specified, distance is 0. The form of the function call is

HomogeneousWaveguide(bfield, species, ground)

HomogeneousWaveguide should be used when modeling with only a single homogeneous waveguide (ground, ionosphere, and magnetic field) along the propagation path.

To model an inhomogeneous propagation path, there is a SegmentedWaveguide type. The SegmentedWaveguide is simply a wrapper for a Vector of waveguides.

Let's look at the components of a waveguide.

BField

The BField type describes the magnitude and direction of the background magnetic field. Internally it consists of fields for the field strength B in Teslas and direction cosines corresponding to the directions parallel, perpendicular, and up into the waveguide.

A BField is most commonly constructed by specifying the field strength, dip angle in radians from the horizontal and positive when directed into Earth, and azimuth angle in radians from the propagation direction, positive towards $y$.

For example,

bfield = BField(50000e-9, π/2, 0)
BField(5.0e-5, 6.123233995736766e-17, 0.0, -1.0)

bfield is a vertical magnetic field of 50,000 nT.

Species

The Species struct identifies a constituent species of the ionosphere. Species contains the fields

numberdensity and collisionfrequency should be "callables" (usually Functions) that return the number density and collision frequency, respectively, as a function of height in meters.

For convenience, the Wait and Spies profile is accessible via waitprofile. Similarly the accompanying collision frequency profiles are electroncollisionfrequency and ioncollisionfrequency.

To define some electrons for the ionosphere (QE and ME were explicitly imported at the top of the example):

h = 75
 β = 0.35
 
-electrons = Species(QE, ME, z->waitprofile(z, h, β), electroncollisionfrequency)
Species(-1.602176634e-19, 9.1093837015e-31, FunctionWrappers.FunctionWrapper{Float64, Tuple{Float64}}(Ptr{Nothing} @0x0000763071f813b0, Ptr{Nothing} @0x00007630168ac068, Base.RefValue{Main.var"#1#2"}(Main.var"#1#2"()), Main.var"#1#2"), FunctionWrappers.FunctionWrapper{Float64, Tuple{Float64}}(Ptr{Nothing} @0x0000763071f81700, Ptr{Nothing} @0x00007630168ac070, Base.RefValue{typeof(electroncollisionfrequency)}(LongwaveModePropagator.electroncollisionfrequency), typeof(electroncollisionfrequency)))

Note that we used a lambda function to specify the waitprofile with our given $h'$ and $\beta$. Also note that these two parameters are a rare instance of SI units not strictly being followed. See the help for waitprofile for more information, including optional height cutoff and density threshold arguments.

electroncollisionfrequency is a function of height z only, so it is not necessary to generate a lambda function. We can pass the function handle directly.

Ground

Ground describes the relative permittivity ϵᵣ and conductivity σ of Earth.

ground = Ground(10, 2e-4)
Ground(10, 0.0002)

For convenience, a dictionary of common ground indices is exported.

GROUND
Dict{Int64, Ground} with 10 entries:
+electrons = Species(QE, ME, z->waitprofile(z, h, β), electroncollisionfrequency)
Species(-1.602176634e-19, 9.1093837015e-31, FunctionWrappers.FunctionWrapper{Float64, Tuple{Float64}}(Ptr{Nothing} @0x00007fc886981290, Ptr{Nothing} @0x00007fc8256c8070, Base.RefValue{Main.var"#1#2"}(Main.var"#1#2"()), Main.var"#1#2"), FunctionWrappers.FunctionWrapper{Float64, Tuple{Float64}}(Ptr{Nothing} @0x00007fc8869815e0, Ptr{Nothing} @0x00007fc8256c8078, Base.RefValue{typeof(electroncollisionfrequency)}(LongwaveModePropagator.electroncollisionfrequency), typeof(electroncollisionfrequency)))

Note that we used a lambda function to specify the waitprofile with our given $h'$ and $\beta$. Also note that these two parameters are a rare instance of SI units not strictly being followed. See the help for waitprofile for more information, including optional height cutoff and density threshold arguments.

electroncollisionfrequency is a function of height z only, so it is not necessary to generate a lambda function. We can pass the function handle directly.

Ground

Ground describes the relative permittivity ϵᵣ and conductivity σ of Earth.

ground = Ground(10, 2e-4)
Ground(10, 0.0002)

For convenience, a dictionary of common ground indices is exported.

GROUND
Dict{Int64, Ground} with 10 entries:
   5  => Ground(15, 0.001)
   4  => Ground(10, 0.0003)
   6  => Ground(15, 0.003)
@@ -42,7 +42,7 @@
 electrons = Species(QE, ME, z->waitprofile(z, 75, 0.35), electroncollisionfrequency)
 ground = GROUND[5]
 
-waveguide = HomogeneousWaveguide(bfield, electrons, ground)
HomogeneousWaveguide{Species}(BField(5.0e-5, 6.123233995736766e-17, 0.0, -1.0), Species(-1.602176634e-19, 9.1093837015e-31, FunctionWrappers.FunctionWrapper{Float64, Tuple{Float64}}(Ptr{Nothing} @0x0000763071f87540, Ptr{Nothing} @0x00007630168ac078, Base.RefValue{Main.var"#3#4"}(Main.var"#3#4"()), Main.var"#3#4"), FunctionWrappers.FunctionWrapper{Float64, Tuple{Float64}}(Ptr{Nothing} @0x0000763071f81700, Ptr{Nothing} @0x00007630168ac080, Base.RefValue{typeof(electroncollisionfrequency)}(LongwaveModePropagator.electroncollisionfrequency), typeof(electroncollisionfrequency))), Ground(15, 0.001), 0.0)

The propagate function returns a tuple of complex electric field, amplitude in dB μV/m, and phase in radians.

E, a, p = propagate(waveguide, tx, rx);

Here are quick plots of the amplitude

plot(ranges/1000, a;
+waveguide = HomogeneousWaveguide(bfield, electrons, ground)
HomogeneousWaveguide{Species}(BField(5.0e-5, 6.123233995736766e-17, 0.0, -1.0), Species(-1.602176634e-19, 9.1093837015e-31, FunctionWrappers.FunctionWrapper{Float64, Tuple{Float64}}(Ptr{Nothing} @0x00007fc886987420, Ptr{Nothing} @0x00007fc8256c8068, Base.RefValue{Main.var"#3#4"}(Main.var"#3#4"()), Main.var"#3#4"), FunctionWrappers.FunctionWrapper{Float64, Tuple{Float64}}(Ptr{Nothing} @0x00007fc8869815e0, Ptr{Nothing} @0x00007fc8256c8080, Base.RefValue{typeof(electroncollisionfrequency)}(LongwaveModePropagator.electroncollisionfrequency), typeof(electroncollisionfrequency))), Ground(15, 0.001), 0.0)

The propagate function returns a tuple of complex electric field, amplitude in dB μV/m, and phase in radians.

E, a, p = propagate(waveguide, tx, rx);

Here are quick plots of the amplitude

plot(ranges/1000, a;
      xlabel="range (km)", ylabel="amplitude (dB)",
      linewidth=1.5, legend=false)

and phase.

plot(ranges/1000, rad2deg.(p);
      xlabel="range (km)", ylabel="phase (deg)",
@@ -79,4 +79,4 @@
   wavefieldheights: StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}
   wavefieldintegrationparams: IntegrationParams{OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}}
   radiationresistancecorrection: Bool false
-

An instance of LMPParams can be passed as the params argument of propagate or findmodes.

See the Parameters.jl README for other ways of interacting with LMPParams.


This page was generated using Literate.jl.

+

An instance of LMPParams can be passed as the params argument of propagate or findmodes.

See the Parameters.jl README for other ways of interacting with LMPParams.


This page was generated using Literate.jl.

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jgf_0Z7^$KhHoKtY_xblSp)yKHTLhEc76$)iI7j{uSCC+} diff --git a/dev/generated/ground/index.html b/dev/generated/ground/index.html index 9379e7f..8fa945e 100644 --- a/dev/generated/ground/index.html +++ b/dev/generated/ground/index.html @@ -43,4 +43,4 @@ p = plot() buildplots!(p, amps) plot!(p; size=(600,400), ylims=(0, 95), title="Night", legend=(0.85, 1.02), - xlabel="Range (km)", ylabel="Amplitude (dB)", legendtitle="ϵᵣ, σ")

Low ground conductivity can have a significant influence on the signal propagation - there is strong attenuation. These low conductivities can be found in areas of sea or polar ice and industrial or city areas.

The influence of ground conductivity on the received signal has similar impact on the day and night scenarios.


This page was generated using Literate.jl.

+ xlabel="Range (km)", ylabel="Amplitude (dB)", legendtitle="ϵᵣ, σ")

Low ground conductivity can have a significant influence on the signal propagation - there is strong attenuation. These low conductivities can be found in areas of sea or polar ice and industrial or city areas.

The influence of ground conductivity on the received signal has similar impact on the day and night scenarios.


This page was generated using Literate.jl.

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cel%+`{qSVbfoCD}Fnf;J6uf0a^}0mSKj}d4o&W#< diff --git a/dev/generated/integratedreflection/index.html b/dev/generated/integratedreflection/index.html index b7438e8..976e4a4 100644 --- a/dev/generated/integratedreflection/index.html +++ b/dev/generated/integratedreflection/index.html @@ -138,4 +138,4 @@ heatmap(tolerancestrings, solverstrings, permutedims(mean_times)/1e6; clims=(0, 5), xlabel="tolerance", ylabel="solver", - colorbar_title="time (μs)", colorbar=true)

The best accuracy occurs with Vern7 and experiment's we've done looking at the sensitivity of the mode solutions to integration tolerance have shown we can get away with a tolerance of 1e-4. To play it safe, the default used by LMP is 1e-5. The integration accuracy improves considerably for relatively little additional computation time if the tolerance is changed to 1e-9, but that accuracy is not required.


This page was generated using Literate.jl.

+ colorbar_title="time (μs)", colorbar=true)

The best accuracy occurs with Vern7 and experiment's we've done looking at the sensitivity of the mode solutions to integration tolerance have shown we can get away with a tolerance of 1e-4. To play it safe, the default used by LMP is 1e-5. The integration accuracy improves considerably for relatively little additional computation time if the tolerance is changed to 1e-9, but that accuracy is not required.


This page was generated using Literate.jl.

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b/dev/generated/interpolatingfunctions/index.html @@ -94,8 +94,8 @@ plot(p1, p2, layout=grid(2,1,heights=[0.7, 0.3]))

Here is the mean absolute amplitude difference between each technique and the true profile amplitude. We filter to finite values because the amplitude calculated at 0 meters is Inf.

for n in ("linear", "cubic", "FritschButland", "FritschCarlson", "Steffen")
     @printf("%s: %.3e\n",n, meanad(filter(isfinite,results[n][2]),
         filter(isfinite,results["truth"][2])))
-end
linear: 1.396e-02
-cubic: 2.647e-03
-FritschButland: 2.776e-03
-FritschCarlson: 2.791e-03
-Steffen: 3.258e-03

The amplitude and phase for each of the interpolators matches the true exponential profile extremely closely relative to the typical noise of real VLF measurements.

Timing can vary when run by GitHub to build the documentation, so results here are from a local run:

InterpolatorRuntime relative to truth
truth1
linear0.84
cubic0.85
FritschButland0.91
FritschCarlson0.92
Steffen0.82

Really, any of these except for the linear interpolation could be used to interpolate a discrete profile. The Steffen and cubic interpolations are fastest, but the FritschButland is a little more true to the actual profile. It's for that reason that FritschButland is used to interpolate TableInput types in LongwaveModePropagator.


This page was generated using Literate.jl.

+end
linear: 1.614e-02
+cubic: 6.315e-03
+FritschButland: 4.328e-03
+FritschCarlson: 5.099e-03
+Steffen: 4.154e-03

The amplitude and phase for each of the interpolators matches the true exponential profile extremely closely relative to the typical noise of real VLF measurements.

Timing can vary when run by GitHub to build the documentation, so results here are from a local run:

InterpolatorRuntime relative to truth
truth1
linear0.84
cubic0.85
FritschButland0.91
FritschCarlson0.92
Steffen0.82

Really, any of these except for the linear interpolation could be used to interpolate a discrete profile. The Steffen and cubic interpolations are fastest, but the FritschButland is a little more true to the actual profile. It's for that reason that FritschButland is used to interpolate TableInput types in LongwaveModePropagator.


This page was generated using Literate.jl.

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b/dev/generated/interpretinghpbeta/index.html @@ -161,4 +161,4 @@ end buildplots!(p, amps); plot!(p; size=(600,400), ylims=(22, 95), - xlabel="Range (km)", ylabel="Amplitude (dB)", legendtitle="1.816 ν₀, a")


    This page was generated using Literate.jl.

    • 1As a government technical report and not a journal paper curated by a publishing company, it is difficult to track how many times it has been cited by others.
    + xlabel="Range (km)", ylabel="Amplitude (dB)", legendtitle="1.816 ν₀, a")


    This page was generated using Literate.jl.

    • 1As a government technical report and not a journal paper curated by a publishing company, it is difficult to track how many times it has been cited by others.
    diff --git a/dev/generated/io/index.html b/dev/generated/io/index.html index e713777..a992853 100644 --- a/dev/generated/io/index.html +++ b/dev/generated/io/index.html @@ -173,7 +173,7 @@ 900000, 1000000 ] -}

    BatchInput

    Both the ExponentialInput and TableInput types can be collected together in a BatchInput which has fields for a name, description, datetime, and vector of Inputs. This is useful for keeping a set of scenarios together. See the test/IO.jl file for additional help on how these should be formatted.

    Running the model from a JSON file

    To run the model, propagate accepts a filename input (see the help for optional arguments). However, instead of returning a tuple of complex electric field, amplitude, and phase, it returns an Output type. Additionally, it saves the output to a JSON file.

    output = propagate(filename);

    Outputs

    There are only two LongwaveModePropagator.Output types: BasicOutput and BatchOutput. Both ExponentialInputs and TableInputs create BasicOutputs, but the BatchInput creates a BatchOutput.

    The BasicOutput contains fields for

    • name::String
    • description::String
    • datetime::DateTime
    • output_ranges::Vector{Float64}
    • amplitude::Vector{Float64}
    • phase::Vector{Float64}

    where name and description are directly copied from the input and datetime is when the model was run.

    output
    BasicOutput("basic", "Test ExponentialInput", Dates.DateTime("2024-03-16T05:36:47.696"), [0.0, 100000.0, 200000.0, 300000.0, 400000.0, 500000.0, 600000.0, 700000.0, 800000.0, 900000.0, 1.0e6], [0.0, 69.0422209373873, 63.22960630343484, 60.32692576011322, 52.46122800119692, 56.88034398278663, 54.30222245936574, 47.34843486581329, 40.459413291030714, 40.88025467719066, 43.8123104785962], [0.7853981633974483, 1.9977776128507398, 1.744763177858933, 1.6657027389205428, 1.087507387578484, 1.2322178477902987, 1.664225992977897, 2.061413457330575, 2.690613816419203, 4.464992218244768, 5.0671281550666105])

    Not surprisingly, a BatchOutput is simply a container holding a Vector of BasicOutputs, as well as some additional metadata from the corresponding BatchInput.

    JSON I/O from Matlab

    Here's an example of how to encode the above ExponentialInput to JSON and decode the output using Matlab. It's also in the file examples/io.m.

    % Matlab script
    +}

    BatchInput

    Both the ExponentialInput and TableInput types can be collected together in a BatchInput which has fields for a name, description, datetime, and vector of Inputs. This is useful for keeping a set of scenarios together. See the test/IO.jl file for additional help on how these should be formatted.

    Running the model from a JSON file

    To run the model, propagate accepts a filename input (see the help for optional arguments). However, instead of returning a tuple of complex electric field, amplitude, and phase, it returns an Output type. Additionally, it saves the output to a JSON file.

    output = propagate(filename);

    Outputs

    There are only two LongwaveModePropagator.Output types: BasicOutput and BatchOutput. Both ExponentialInputs and TableInputs create BasicOutputs, but the BatchInput creates a BatchOutput.

    The BasicOutput contains fields for

    • name::String
    • description::String
    • datetime::DateTime
    • output_ranges::Vector{Float64}
    • amplitude::Vector{Float64}
    • phase::Vector{Float64}

    where name and description are directly copied from the input and datetime is when the model was run.

    output
    BasicOutput("basic", "Test ExponentialInput", Dates.DateTime("2024-03-22T00:26:25.582"), [0.0, 100000.0, 200000.0, 300000.0, 400000.0, 500000.0, 600000.0, 700000.0, 800000.0, 900000.0, 1.0e6], [0.0, 69.03793070620536, 63.23417345887722, 60.32545411257551, 52.463979714590664, 56.883072656141884, 54.30149029776226, 47.34877154362522, 40.46102741446798, 40.87896697013488, 43.810027346338245], [0.7853981633974483, 1.9977501255480048, 1.7445362124076118, 1.6657354711950825, 1.0869981959615773, 1.2323543807678279, 1.6642027856966908, 2.0611344533705203, 2.6901388711083407, 4.465200767571669, 5.067248706976456])

    Not surprisingly, a BatchOutput is simply a container holding a Vector of BasicOutputs, as well as some additional metadata from the corresponding BatchInput.

    JSON I/O from Matlab

    Here's an example of how to encode the above ExponentialInput to JSON and decode the output using Matlab. It's also in the file examples/io.m.

    % Matlab script
     
     input.name = "basic";
     input.description = "Test ExponentialInput";
    @@ -227,4 +227,4 @@
     
     with open('basic_python.json', 'w') as file:
         file.write(json_str)

    Let's ensure that the JSON file is correctly parsed.

    python_input = LMP.parse(joinpath(examples_dir, "basic_python.json"))
    ExponentialInput("basic", "Test ExponentialInput", Dates.DateTime("2020-12-29T11:35:11.989"), [0.0], [75.0], [0.35], [5.0e-5], [1.5707963267948966], [0.0], [0.001], [4], 24000.0, [0.0, 100000.0, 200000.0, 300000.0, 400000.0, 500000.0, 600000.0, 700000.0, 800000.0, 900000.0])

    And run the file.

    python_output = propagate(joinpath(examples_dir, "basic_python.json"));

    To read the results:

    with open('basic_python_output.json', 'r') as file:
    -    output = json.load(file)

    This page was generated using Literate.jl.

    + output = json.load(file)

    This page was generated using Literate.jl.

    diff --git a/dev/generated/magneticfield/index.html b/dev/generated/magneticfield/index.html index 694ffa2..e1faa8a 100644 --- a/dev/generated/magneticfield/index.html +++ b/dev/generated/magneticfield/index.html @@ -156,4 +156,4 @@ plot(OUTPUT_RANGES/1000, agrid; linewidth=1.5, palette=colors, colorbar=false, xlabel="range (km)", ylabel="amplitude (dB)", - labels=permutedims(labels), legendtitle=" dip, az", legend=true)
    
    Progress:  22%|█████████▏                               |  ETA: 0:00:42
    Progress:  33%|█████████████▋                           |  ETA: 0:00:40
    Progress:  44%|██████████████████▎                      |  ETA: 0:00:32
    Progress:  56%|██████████████████████▊                  |  ETA: 0:00:26
    Progress:  67%|███████████████████████████▍             |  ETA: 0:00:19
    Progress:  78%|███████████████████████████████▉         |  ETA: 0:00:13
    Progress:  89%|████████████████████████████████████▌    |  ETA: 0:00:06
    Progress: 100%|█████████████████████████████████████████| Time: 0:00:57

    At these lower reflection altitudes the effect of Earth's magnetic field is decreased.


    This page was generated using Literate.jl.

    + labels=permutedims(labels), legendtitle=" dip, az", legend=true)
    
    Progress:  22%|█████████▏                               |  ETA: 0:00:42
    Progress:  33%|█████████████▋                           |  ETA: 0:00:38
    Progress:  44%|██████████████████▎                      |  ETA: 0:00:31
    Progress:  56%|██████████████████████▊                  |  ETA: 0:00:26
    Progress:  67%|███████████████████████████▍             |  ETA: 0:00:19
    Progress:  78%|███████████████████████████████▉         |  ETA: 0:00:13
    Progress:  89%|████████████████████████████████████▌    |  ETA: 0:00:06
    Progress: 100%|█████████████████████████████████████████| Time: 0:00:56

    At these lower reflection altitudes the effect of Earth's magnetic field is decreased.


    This page was generated using Literate.jl.

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