Space Weather Flashcards

1
Q

What region defines the near geospace

A

Up to around 200 Re

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2
Q

What are the regions of the space environment

A

Troposphere
Stratosphere
Mesosphere
Thermosphere
Ionosphere
Exosphere
Plasmasphere
Magnetosphere

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3
Q

What is a characteristic of dispersive waves

A

Angular frequency is a function of the wave number k

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4
Q

Why does the Lorentz force arise

A

Interactions when a charged particle moves in an electric and magnetic field

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5
Q

What is bulk ion plasma velocity

A

Average velocity of plasma ions

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6
Q

At thermal equilibrium what does each degree of freedom relate to

A

kT/2

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7
Q

What does the Debye length mean

A

Spatial charge separation scale in plasma

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8
Q

What are the 3 plasma criteria

A

Debye length much smaller than system spatial scale
The parameter must be much greater than 1
The time between collisions between neutral and charged particles must be much longer than the period of oscillations at plasma frequency

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9
Q

What physical parameters affect Larmor radius in uniform and constant electric and magnetic fields

A

Larger mass particles will have a larger Larmor radius
Higher energy particles will have a larger Larmor radius

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10
Q

What kind of drift is independent of charge

A

Electric field drift - all particles drift in the same direction with average displacement perpendicular to electric field direction

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11
Q

Which drifts are dependent on charge

A

Gravitational field
General force
Gradient

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12
Q

What conditions are needed for GCA to be valid

A

Larmor (cyclotron) frequency must be greater than the wave frequency
Larmor radius is much smaller than spatial scale of the system

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13
Q

How does the first adiabatic invariant come about and what does it mean

A

Comparing dynamical and mechanical systems
The perpendicular kinetic energy divided by the magnetic field strength at that point is constant

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14
Q

What happens to velocity at the mirror point

A

The parallel velocity component is 0

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15
Q

What condition must hold for transverse waves to propagate through the ionosphere

A

Angular frequency must be greater than the plasma electron frequency

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16
Q

What are sunspots

A

“Darker” parts on the sun’s surface that are associated with increased solar activity
They are cooler than surroundings and have strong magnetic field

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17
Q

Summarise the layers of solar interior

A

Core - nuclear fusion occurs
Radiative zone - energy from core radiates outwards
Tachocline - transition from rigid to fluid-type rotation generating magnetic field
Convective zone - energy transported by convective currents

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18
Q

How does global magnetic field generation occur

A

Differential rotation
Difference in rotational speed stretches and twists magnetic field lines in plasma causing field to become distorted and wound up over time
Converts poloidal to toroidal magnetic fields

Also turbulent plasma rotation means small-scale twisted magnetic fields generated by solar convection motions

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19
Q

What are the layers of the solar atmosphere

A

Photosphere
Chromosphere
Transition region
Corona

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20
Q

What is the photosphere

A

Surface of sun
Mottled texture due to granules - convection cells

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21
Q

What is the chromosphere

A

Emits hydrogen-alpha light
Filaments, spicules and faculae regions around active areas
Lighter elements with traces of heavier

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22
Q

What is the transition region

A

Variable layer with dramatic temperature rise
Contains ionised atoms

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23
Q

What is the corona

A

Contains highly ionised atoms of iron, neon, oxygen etc.
Produces emission lines in UV and X-ray
Source of solar wind

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24
Q

How is solar wind produced

A

Extremely hot corona causes high energy particles to escape gravitational pull
Ionised particles stream from corona as highly conductive plasma

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25
Q

How does solar wind form interplanetary magnetic field

A

As wind flows outwards carries magnetic field lines with it

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26
Q

Where does fast solar wind originate

A

Regions of open magnetic field liens primarily in coronal holes
Low electron density
High velocity
High proton temp
Low electron temp
High magnetic field

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27
Q

What does slow solar wind do

A

Role in formation of heliospheric current sheet - large scale magnetic boundary that extends through heliosphere

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28
Q

What is Parker spiral

A

Spiral shape of magnetic field that forms from twist due to sun rotation
More distorted during solar maximum

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29
Q

What are stream interaction regions

A

Fast wind piles up behind slow wind so plasma denser and more complex magnetic field

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30
Q

What effects do SIRs have

A

Enhanced auroral activity
Fluctuations in ionosphere interfering with satellite operations and communication

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31
Q

What are solar flares

A

Sudden intense bursts of radiation
Mainly EM radiation and energetic particles
Short lived

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32
Q

What are coronal mass ejections

A

Large scale ejection of plasma and magnetic field
Slow travelling
Plasma cloud expands and moves outward sweeping up solar wind and creates shock waves

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33
Q

What the types of CME

A

Limb CME - headed away from earth - no effect
Partial halo CME - glancing blow on earth - weak geomagnetic storm
Halo CME - headed directly at earth - strong and long geomagnetic storm

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34
Q

What is magnetic reconnection

A

Antiparallel field lines forced towards each other
Fields connect resulting in X-configuration
Field lines cut and connected to those on other side and expelled

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35
Q

How do flares and CMEs cause effects

A

Reconnection during flares can release energy burst that accelerates particles
CME-driven shock wave accelerates particles

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36
Q

What are the types of solar energetic particles

A

Impulsive SEP - short lived, localised, associated with flares, high proportion of heavy ions and electrons, narrow spatial impact

Gradual SEP - long lived, widespread, associated with CMEs, broad range of particle energies, global effects including geo storms

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37
Q

Summarise the structures surrounding earth

A

Bow shock, magnetosheath, magnetopause, polar cusps, tail lobes, neutral sheet

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38
Q

What are the property changes through bow shock

A

Bulk velocity decrease
Density increases (pile-up)
Temperature increase
Pressure increase
Normal magnetic field constant
Tangential magnetic field increase (pile-up)

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39
Q

What are the components of terrestrial bow shock

A

Increased magnetic field - reflects ions and electrons
Increased electrostatic potential - reflects ions, pushes electron through shock front

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40
Q

How does ion reflection work

A

Process for redistribution of energy in front of strong shock
If angle between magnetic field and normal to shock < 45 reflected ions move far away into upstream (quasi-parallel)
If angle > 45 reflect ions turned back by magnetic field

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41
Q

How do spatial scales of quasi-parallel and quasi-perpendicular shocks differ

A

Quasi-parallel shock front many times wider than ion Larmor radius
Quasi-perpendicular about same as ion Larmor radius

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42
Q

How is position of subsolar day time magnetopause position determined

A

Balance of dynamic ram pressure and terrestrial magnetic field pressure

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43
Q

When does reconnection occur between solar wind magnetic field and terrestrial magnetic field

A

When direction of solar magnetic field is directed southward

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44
Q

What is the cusp

A

Separates closed dayside magnetic field lines from nightside
Region of easy access for solar wind ions into magnetosphere

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45
Q

What is the magnetotail

A

Region on night side where magnetic field lines are elongated
Contains north and south tail lobes where density is low

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46
Q

What is the neutral/plasma sheet

A

Separates tail lobes
Layer of weaker magnetic field and denser plasma

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47
Q

What are the magnetospheric currents

A

Cross tail - flows across neutral sheet from dawn to dusk
Nightside magnetopause - closes cross tail current
Dayside magnetopause - solar wind electrons/ions deflected in different directions
Field aligned - flow along field lines connecting magnetosphere to ionosphere
Ring - trapped electrons/ions drifting in opposite directions

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48
Q

What happens to particles in magnetospheric magnetic field

A

Move along field lines into regions of stronger field
Pitch angle increases and transverse energy increases
Particle reflected at point where parallel motion is 0 (mirror point)

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49
Q

What effect does pitch angle have on motion

A

Small equatorial pitch angle means large parallel velocity
Mirror points are at high latitudes close to earth and move towards equator with increasing pitch angle
Trapped particles have close to 90 degree angle

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50
Q

What is bounce period

A

Time for a particle to move from equatorial plane to one mirror point, to other mirror point, back to equatorial plane

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51
Q

What is loss cone

A

Region where particles are absorbed rather than reflected
If mirror point is deep in atmosphere particles collide with neutrals and are absorbed
Equatorial loss con defines pitch angle where particles with a smaller angle are lost to atmosphere

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52
Q

What is the ring current

A

Toroidal west flowing electric current with variable density
Satellites build surface charge in it

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53
Q

What are the regions of radiation belts

A

Inner belt - protons, electrons and ions, stable, occasional perturbation from geo storms
Outer belt - mostly high energy electrons, dynamic, produced by injection and energisation events following geo storms
Slot region

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54
Q

Summarise radiation belt characteristics

A

Formed from solar wind particles entering outer magnetosphere or plasma sheet
Accelerated by local wave-particle interaction resonance
Losses from: Coulomb collision in plasma/ionosphere, magnetopause shadowing, scattering of particles by wave-particle interaction in loss cone

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55
Q

Summarise ionosphere formulation

A

Plasma from ionisation of atmosphere molecules by solar photons
UV absorbed so intensity decreases - rate of ion production proportional to radiation absorbed
Intensity inc. with height, density dec. with height
Electron/ion density overall increase through D and E layer, decrease at sporadic E, increase through F with maximum at F2, decrease through top layer

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56
Q

What are sources of solar weather

A

Fast and slow solar wind, CME, solar flares

Cosmic rays, soft gamma repeaters, gamma ray bursts

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57
Q

How is solar wind accelerated

A

Pressure gradient between corona and distant point in space

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58
Q

What is co-rotating interaction region

A

When corona is quasi-stable, solar rotation produces series of SIRs which impact on earth every 27 days (sun axis rotation time)

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59
Q

How do SIRs affect technology

A

Enhancement of energetic electrons in radiation belts
Geo magnetic storms cause aurora and heat thermosphere increasing density (drag)

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60
Q

How do CMEs affect technology

A

Cause strong geomagnetic storms that affect transformers, rail networks, oil and gas pipelines, LEO drag

Also SEP events on solar panels, aircraft

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61
Q

How is solar wind measured

A

Spacecraft in upstream Lagrange point

62
Q

How do solar flares affect technology

A

Increased ionisation leads to radio blackouts, degradation of solar panels, heating of thermosphere

63
Q

How do galactic cosmic rays cause problems

A

High energy particles accelerated meaning deeper penetration in atmosphere, collide with neutral particles and create secondary SEPs

64
Q

What are soft gamma repeaters

A

Emit large bursts of gamma and X-rays irregularly

65
Q

What is Ampere’s circuit law and how is it applicable to ring current

A

Electric current creates a magnetic field that encircles the current and is perpendicular

Magnetic field strength is proportional to the current and inversely proportional to distance from current centre

Ring current will create a magnetic field that is in opposite direction to terrestrial magnetic field

66
Q

What is the Dst index

A

Quantifies the strength of geomagnetic storms

67
Q

How are Dst calculations performed

A

Find a baseline
Eliminate solar quiet daily variations
Average over values obtained from four observatories

68
Q

What is the Kp index

A

Reflects variations of geomagnetic field with respect to quiet day variations
Measured on quasi-logarithmic scale
Calculated every 3 hours using values for K-indices from 13 observatories

69
Q

What can geo storms affect

A

Drilling that uses geomagnetic measurements for guidance
Surveying of subsurface features using magnetic field measurements

70
Q

How is the field aligned current quantified

A

Amplitude upper/lower (AU/AL) are the envelopes of superposition of recordings from observatories
Auroral electrojet (AE) is difference between AU and AL
AO index is average of AU and AL

71
Q

How does solar wind power magnetosphere and storm time dynamics

A

Kinetic energy flux - shaping of magnetosphere, inefficient
Poynting flux - EM power delivered by reconnection, efficiency determined by angle of solar wind magnetic field and shaping of magnetosphere

72
Q

What are effects of geo storms on technology

A

Geomagnetically induced currents
Atmospheric drag
Ionospheric disturbances
Magnetic altitude control

73
Q

What is Faraday’s law of induction and what is effect on field aligned current

A

Time varying magnetic field induces an electric field
Auroral electrojets are time varying currents that generate time varying magnetic field (Ampere’s law)
This in turn generates an electric field

74
Q

How does the field aligned current cause GICs and what impact do they have

A

Generates electric field causing GICs to flow in conducting material
Can flow in power systems as quasi-DC current
Flow through transformer winding, extra magnetisation when AC current in same direction as GIC, saturates iron core and excess heat dissipation damages system

Also affect cathode corrosion protection in pipelines, railways with automatic traffic signals and safety equipment, cable outages in telecoms

75
Q

What is relationship between group and phase velocity with speed of sound and plasma frequency

A

When wave frequency is much greater than plasma frequency both velocities are equal to speed f light

If wave frequency is greater but in same order as plasma frequency, group velocity slows down as is smaller in same order as speed of light, phase velocity speeds up and is greater but in same order as light speed - photons move at group velocity

76
Q

What is the refractive index physically representing

A

Ratio of wave speed in a vacuum to the wave speed in the medium

77
Q

What causes ionospheric plasma

A

Ionisation of atmospheric molecules by solar photons

78
Q

What is the refractive index of neutral atmosphere and how does the refractive index vary with electron density in ionosphere

A

N = 1
As altitude increases so does electron density up to maximum value, plasma frequency increases to this point and so refractive index decreases

79
Q

How is a radio wave reflected in the ionosphere

A

The angle relative to ionosphere normal is 90 degrees at the apex of trajectory

80
Q

What is the critical frequency of an ionospheric layer

A

Highest frequency that reflects at a vertical incidence
Vertical incidence has 0 degree angle
Refractive index is 0 when plasma frequency = wave frequency
Reflection occurs when phase velocity is infinite and group velocity is 0

81
Q

When are waves absorbed and when are waves reflected in the ionosphere

A

Absorbed when wave frequency < plasma frequency
Reflected when wave frequency < critical frequency

82
Q

How can ionospheric electron density be found

A

Reflection of radio waves
Ionosonde generates vertical radio pulses
Travel time is determined to calculate distance to reflection point
By varying pulse frequency a plot of frequency vs height can be obtained

83
Q

What are the characteristics of ionosphere D layer

A

Lowest layer
Results from ionisation of nitrogen and oxygen by X-rays and NO by Lyman-alpha
Low altitude = high recombination rate
High concentration of neutrals

84
Q

What does a high concentration of neutrals cause

A

Waves cause passing ions and electrons to oscillate and collide with neutrals
Collisions dampen oscillations so energy absorbed from radio wave
Lower frequency = greater damping and signal absorption

85
Q

What causes the formation of the F layer

A

Ionisation of oxygen and hydrogen by UV

86
Q

What is the lowest usable frequency

A

Frequency below which the D-layer absorbs the signal

87
Q

What is the maximum usable frequency

A

Frequency above which the wave will not reflect in F-layer

88
Q

What is the relationship between ionospheric effects and frequency

A

Effects decrease as frequency increases

89
Q

How are radio blackouts caused

A

SEPs guided into polar regions
Collide with atmospheric neutrals and produce ions and electrons
Prevalent in D layer

90
Q

How do GNSS determine their position at a specific time

A

Atomic clocks for accurate time
Use ground stations to determine position

91
Q

How are GNSS used to for navigation

A

They emit signals containing satellite identifier, time of emission and position
Time delay in receiving determines distance to satellite
Trilateration to calculate position but 4th needed to correct receiver clock errors

92
Q

What causes the difference between the geometric path of propagation and the actual path

A

Group velocity is different to speed of light so signal delayed in ionosphere compared to vacuum propagation

93
Q

What is total electron content

A

Integral of electron density with respect to the signal path
Time delay is proportional to TEC and inversely proportional to square of wave frequency

94
Q

When does excess range error occur

A

If distance between receiver and GNSS is determined using vacuum speed of light
Error increases with non-vertical incidence

95
Q

How can TEC be estimated and why does this work

A

Using two frequencies of signal
Ionosphere is dispersive with frequency dependence

96
Q

What is ionising radiation

A

Has sufficient energy to free electrons
E.g. UV, X-rays, gamma rays
Causes displacement damage and total ionisation dose damage

97
Q

What is non-ionising radiation

A

Sufficient energy to produce damage by heat or atomic damage
E.g. radio waves, microwaves, visible light
Causes non-ionising thermal damage, displacement damage and cell damage

98
Q

What is total ionisation dose damage

A

Cumulative changing of electrical parameters
Single event phenomena are circuit upsets or changes

99
Q

What is the relationship between electrical components and radiation resistance

A

Passive components are more resistant to radiation (resistors, capacitors, inductors)

Active components are more susceptible to radiation (transistors, integrated circuits, diodes)

100
Q

What does the threshold for ionising radiation mean

A

The energy required to remove external electron
Dependent on the atom

101
Q

What is the photoelectric effect

A

Interactions between incident photon and bound electron
Electron receives whole energy of photon and is ejected from atom
Dominant for photons < 50 keV

102
Q

What is Compton scattering

A

Electron is ejected after receiving fraction of photon energy
Rest of energy is emitted as a lower energy photon
Dominant energy transfer process between 50 keV and 5 MeV

103
Q

What is pair production

A

Interaction of incident photon and atomic nucleus results in electron-positron pair
Dominant for photons > 5 MeV

104
Q

What are the characteristics of photon flux absorption

A

Absorption increases with thickness of material
Increases with linear attenuation coefficient
Coefficient decreases for higher energy photons

105
Q

How are spacecraft surfaces charged

A

Sun lit surfaces are positively charged due to photoelectric effect
Shaded surfaces are negatively charged due to electron flux
Occurs when there is an imbalance of electric currents

106
Q

How is spacecraft potential determined

A

Balance of different currents e.g. incidence electron and ion current, photoelectron current, secondary emitted electron currents
A system in equilibrium has 0 total electric current

107
Q

How is spacecraft charging mitigated

A

Set maximum potential difference
Electrically connect structural and mechanical parts with lower resistance to ground them

108
Q

When is a particle’s energy increased

A

When electric field is in same direction of motion

109
Q

What is magnetic rigidity of a charged particle

A

Quantifies the ability of a charged particle to penetrate magnetic field
Energy of a particle is the sum of its rest mass and its kinetic energy

110
Q

What is magnetic rigidity cut-off

A

Particles with high magnetic rigidity are harder for geomagnetic field to deflect
Cut-off corresponds to threshold value of magnetic rigidity to access a particular point in region of magnetic field
Usually expressed in GV

111
Q

What is excitation and de-excitation

A

Charged particle transfers energy to an electron in the atom, not enough to ionise but increases electron energy state
Electron emits a photon when returning to original energy state

112
Q

What is Bremsstrahlung radiation

A

Breaking radiation
Charged particle transfers energy to nucleus accelerating it
Nucleus slows down by releasing radiation

113
Q

What is electrostatic force

A

Main mechanism of interaction between a charged particle that travels through continuous medium and atoms of the medium

114
Q

What is stopping power and range of a material

A

Energy lost per unit of distance when a charged particle moves through medium

Depth of penetration of a particle

115
Q

What is the effect of radiation on electronic components

A

Production of impurities
Radiolysis (chemical breakdown)
Ionisation
Atom displacement within lattice structure

116
Q

What types of damage from radiation are there

A

Single event effects (non-destructive and potentially destructive)
Deep dielectric charging/discharge
Displacement damage
Total ionising dose

117
Q

Why do we need to forecast space weather what do we need to forecast

A

To mitigate effects on technological systems that are important for infrastructure

Parameters that affect technology operation and indices that characterise strength of disturbance

118
Q

What methods are there to forecast

A

Physics/first principles based - taking physical knowledge, first principles and assumptions to come up with equations that describe situations, build these into numerical code for models

Data driven - taking input data, physical knowledge and output data to come up with an algorithm to model situations, use physical understanding to see how well it fits

119
Q

Why can physics based models be computationally expensive

A

Models of complex systems often don’t have exact solutions and have to be solved numerically with discretisation in time and space

120
Q

What types of models come under data driven branch

A

Linear regression
System identification
Machine learning

121
Q

Which Lagrange point is used to forecast and why

A

L1
Solar wind will impact on satellite there around an hour before impacting on earth

122
Q

What is the range of measurement for prediction efficiency

A

Minus infinity to 1

123
Q

What is the range of measurement for correlation

124
Q

What are binary skill scores

A

Metrics deduced from prediction of a binary event (event happens or it doesn’t)

125
Q

What do the 4 quadrants in a binary skill score represent

A

X - successful predictions the event happens (Hit)
Z - false prediction the event happens (False alarm)
Y - incorrect prediction the event doesn’t happen (Miss)
W - successful prediction the event doesn’t happen (Correct rejection)

126
Q

What challenges exist with space weather forecasting

A

Reliable forecasts from the Sun to L1 to allow longer lead time
Forecasting GICs
Forecasting strong solar flares and CME eruptions

127
Q

How is the phase velocity of a dispersive wave found

A

Divide the wave frequency by k (wave number)

128
Q

How is the group velocity of a dispersive wave found

A

Take the partial derivative of wave frequency with respect to k

129
Q

What is the cross product of two vectors A x B

A

Equal to determinant of 3x3 matrix with top row elements equal to x, y, z components of A, middle row elements equal to x, y, z components of B, bottom row elements equal to directional vectors in x, y, z direction

130
Q

What calculations must be done for plasma criteria

A

Calculate the Debye length and check &laquo_space;spatial scale
Calculate electron density * Debye length cubed and check&raquo_space; 1
Calculate plasma frequency * period of collisions and check&raquo_space; 1

131
Q

What calculations must be done for guiding centre approximation

A

Calculate cyclotron/Larmor frequency and check > wave frequency
Calculate Larmor radius and check &laquo_space;spatial scale to find perpendicular velocity requirement for GCA

132
Q

What is the pitch angle equal to mathematicaly

A

Arctan of perpendicular/parallel velocity

133
Q

What does the first adiabatic invariant mean and what can it be used for

A

Ratio of perpendicular kinetic energy/magnetic field strength is constant
Can find the velocity or field strength at a point given conditions

134
Q

How is the angle or field strength at a mirror point found

A

Use first adiabatic invariant
Set up energy conservation
Replace mirror perpendicular velocity using adiabatic invariant
Rearrange for the parallel velocity at mirror point and set equal to 0

135
Q

How is the spatial scale of a system calculated and what is done to compare with Larmor radius

A

Lambda = 2 * pi/k
Half * lambda to compare with Larmor radius

136
Q

What is the speed of sound in plasma

A

sqrt(2kbT/m)

137
Q

How are questions about the position of day time sub solar magnetopause solved

A

Set the dynamic ram pressure equal to the terrestrial magnetic field pressure
Find the strength of magnetic field using known equation and coefficient factor
Rearrange for the parameter of interest e.g. solar wind velocity

138
Q

What is the relationship between magnetic field strength at points and the pitch angle at points

A

B1/B2 = (sin(a1)/sin(a2)^2

139
Q

What is the thermal velocity of solar wind and how is it calculated

A

Vth = sqrt(2kbt/m)
Equate kinetic energy and thermal energy

140
Q

What is the escape velocity and how is it calculated

A

Vesc = sqrt(2GM/r)
Equate kinetic energy with gravitational potential energy

141
Q

How is the minimum electron density for radio wave reflection found

A

Use Snell’s law for reflection so sin(incident angle) = N_reflection - because N_incidence = 1 and sin(reflection) = sin(90) = 1
Replace Nr with the ratio of c/Vph and square
Replace sin^2 + 1 = cos^2 and multiply wave frequency across
Replace plasma frequency with known equation
Rearrange for electron density
Set incidence angle to 0 for minimum value (cos(0) = 1)

142
Q

How is the time delay in ionosphere calculated

A

Actual path minus geometric path is integral of 1/Vgr - 1/c
Replace for value of Vgr and factor out 1/c
Use binomial approximation to give time delay = 1/2cf^2 * integral of plasma frequency^2 ds
Factor everything out until it is just the integral of electron density which is equal to TEC

143
Q

How is the TEC calculated

A

The time of arrival for a signal is t1 = R/c + time delay_1
Find the time delay using t1 - t2 and rearrange for TEC

144
Q

How is the range of communication found

A

Time of arrival approximated is tv = R/c = t1 - time delay_1
Input expression for time delay and rearrange for range R

145
Q

What are the photon relations for angular frequency, speed of light and wave number

A

w = 2 * pi * f
c = f * wavelength
k = 2 * pi * wavelength

146
Q

What are the photon relations for energy and momentum

A

E = h * f
E/h = c/wavelength
E = h * w/2 * pi
p = h * k/2 * pi
Wavelength = h/p

147
Q

What is the equation for flux density attenuation

A

I = I0 * e^(-mu * x)

148
Q

How is magnetic rigidity calculated

A

Magnetic rigidity is R = p c/q
Energy is E = Ek + mc^2 (Energy = kinetic energy + rest mass)
Equation is E^2 = (pc)^2 + (mc^2)^2
Insert energy sum into equation and expand out then rearrange to get pc = sqrt(Ek^2 + 2
Ekmc^2)
Insert value of pc into magnetic rigidity equation

149
Q

How is the expression for drift velocity calculated using the GCA

A

Establish particle position vector as sum of Larmor radius vector and distance from centre of Larmor rotation
Find the equation of motion under magnetic field and gravitational force influence
Average the motion of period of Larmor rotation so all values of Larmor radius vector and derivatives are 0
Decompose velocity into perpendicular and parallel components
Product of two parallel vector is zero
This leaves only perpendicular components for parallel acceleration is 0 and parallel velocity is constant and 0 because of initial conditions
Assume perpendicular velocity is constant so perpendicular acceleration is 0
Take cross product with B
Use cross product relation to eliminate dot product of perpendicular vectors (equal to 0)
Rearrange for perpendicular velocity

150
Q

In calculator which standard deviation is used

A

Sample standard deviation
Sx
4th option