H - Fusion Flashcards
What is the Virial Theorem? How is it used in star formation?
VT relates the avg KE (K) and the avg PE (U) of a system.
In classical mechanics, for particles interacting through the inverse square law (gravity or EM) then:
• {U} = 2*{K} where {} bra-ket notation
In star clusters, it relates the total kinetic energy of the stars (due to motion) to the total GPE of the system
What is the Jean criterion? What does the equation tell us and how does this differ to reality?
Used to describe the conditions under which gravitational instability leads to the collapse of a cloud of gas or dust to form stars or galaxies.
Jean criterion relates gravitational collapse of a cloud to its mass, size, temperature, and density.
• Mjean = critical mass of a cloud required for gravitational collapse to overcome thermal pressure
• in theory it tells us we could easily obtain 10-100 solar masses, however most observed stars have <1 solar masses
Why - collapse of 1 gas cloud must yield many <1 solar mass stars
• allows astronomers to assume a cluster of stars have same chemistry as they would have formed from same cloud
What are two important scales within a dynamic system? Why? Provide an example.
Length scale and timescales are important
• length - spatial dimension where reactions take place — size of stellar core dictates type of reactions taking place
•timescale - different reactions take place depending on temp, density and pressure.
1H + 1H —> 2H1 + e+ +neu_e ~ 1 bill yrs
1H + 2H1 —> 3He2 + gamma ~ 4 seconds
What is the main sequence of burning in stars? What are the solar masses required to form neutron stars and black holes?
Hydrogen —> Helium —> Carbon (8M) —> Oxygen —> silicon (8-11M) —> Iron
Neutron star - 10-29 solar masses
Black holes - >= 25 solar masses
What is the Gamow Peak?
Explains the probability of nuclear reactions occurring due to QT.
Two particles need to overcome Coulomb repulsion in order to get close enough for the SNF to fuse them together.
Gamow peak represents the maximum of the energy-dependent reaction cross-section at a specific energy range where the probs of tunnelling is highest.
• as temps in stars increase - particles KE increase - tail of energy distribution extends to higher energies - small fraction of particles have sufficient energies to tunnel through the potential barrier
What is the fate of our sun?
Once the primary fuel source (hydrogen) is exhausted, the sun will expand into a red giant
• this will expand past Earths orbit
Suns outer layers will start shedding into space - forming a planetary nebula
The core (mainly composed of Helium) will cool and contract, forming a white dwarf
• over billions of years this will cool and form into a black dwarf
What are the commercial fusion Reactions and their energy production? Pros and cons?
D + D —> 3He2 + n + 3.26MeV
D + D —> 3H1 + p + 4.04MeV
D + T —> 4He2 + n + 17.6MeV
Deuterium - easily accessible in vast quantities (sea)
Tritium - short half life and currently very difficult and expensive to source
What is the Maxwell-Boltzmann distribution describing? How does this impact fusion?
The distribution describes the probability distribution of a particle’s velocity for a given temperature (particles velocity will vary)
MB distribution can help determine the proportion of particles that have enough energy to fuse, alongside the energy required to tunnel through potential barrier the Gamow peak can be determined
What is the reaction rate of fusion proportional to? How is it calculated?
For X + Y —> Z + particle + Q
Reaction rate will be proportional to:
• conc of both X and Y
• cross-section of reaction
• relative velocity of two nuclei, v
Often conscientious to give mean fusion cross-section, averages over all possible velocities {sigma•v} in m3•s-1. This is known as reactivity R.
R = C•n_X•n_Y•{sigma•velocity}
What is the reactivity equation?
R = C•n_X•n_Y•{sigma•velocity}
C = constant
n_x & n_y = densities of nuclei respectively
Sigma - cross-section of reaction
Velocity - related to approaching E (tunnelling energy) and therefore linked to sigma
