Energy Balance

The central concept of the Lawson criterion is an examination of the energy balance for any fusion power plant using a hot plasma. This is shown below: Net power = Efficiency (Fusion Radiation loss Conduction loss) Net power is the excess power beyond that needed internally for the process to proceed in any fusion power plant. Efficiency is how much energy is needed to drive the device and how well it collects energy from the reactions. Fusion is rate of energy generated by the fusion reactions. Radiation loss is the energy lost as light (including X-rays) leaving the plasma. Conduction loss is the energy lost as particles leave the plasma, carrying away energy.Lawson calculated the fusion rate by assuming that the fusion reactor contains a hot plasma cloud which has a Gaussian curve of individual particle energies, a Maxwell-Boltzmann distribution characterized by the plasma's temperature. Based on that assumption, he estimated the first term, the fusion energy being produced, using the volumetric fusion equation. Fusion = Number density of fuel A Number density of fuel B Cross section(Temperature) Energy per reaction Fusion is the rate of fusion energy produced by the plasma Number density is the density in particles per unit volume of the respective fuels (or just one fuel, in some cases) Cross section is a measure of the probability of a fusion event, which is based on the plasma temperature Energy per reaction is the energy released in each fusion reactionThis equation is typically averaged over a population of ions which has a normal distribution. For his analysis, Lawson ignores conduction losses. In reality this is nearly impossible; practically all systems lose energy through mass leaving. Lawson then estimated the radiation losses using the following equation: P B = 1.4 10 34 N 2 T 1 / 2 W c m 3 displaystyle P_B=1.4cdot 10^-34cdot N^2cdot T^1/2frac mathrm W mathrm cm ^3 where N is the number density of the cloud and T is the temperature.

Energy  Balance 1

• Other Related Knowledge ofthe energy balance

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Q-value and energy balance

In writing down the reaction equation, in a way analogous to a chemical equation, one may in addition give the reaction energy on the right side: Target nucleus projectile Final nucleus ejectile Q.For the particular case discussed above, the reaction energy has already been calculated as Q = 22.2 MeV. Hence: 63Li 21H 2 42He 22.2 MeV. The reaction energy (the "Q-value") is positive for exothermal reactions and negative for endothermal reactions, opposite to the similar expression in chemistry. On the one hand, it is the difference between the sums of kinetic energies on the final side and on the initial side. But on the other hand, it is also the difference between the nuclear rest masses on the initial side and on the final side (in this way, we have calculated the Q-value above).

Energy  Balance 2

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Atmospheric energy balance

OLR is a critical component of the Earth's energy budget, and represents the total radiation going to space emitted by the atmosphere. OLR contributes to the net all-wave radiation for a surface which is equal to the sum of shortwave and long-wave down-welling radiation minus the sum of shortwave and long-wave up-welling radiation. The net all-wave radiation balance is dominated by long-wave radiation during the night and during most times of the year in the polar regions. Earth's radiation balance is quite closely achieved since the OLR very nearly equals the Shortwave Absorbed Radiation received at high energy from the sun. Thus, the Earth's average temperature is very nearly stable. The OLR balance is affected by clouds and dust in the atmosphere. Clouds tend to block penetration of long-wave radiation through the cloud and increases cloud albedo, causing a lower flux of long-wave radiation into the atmosphere. This is done by absorption and scattering of the wavelengths representing long-wave radiation since absorption will cause the radiation to stay in the cloud and scattering will reflect the radiation back to earth. the atmosphere generally absorbs long-wave radiation well due to absorption by water vapour, carbon dioxide, and ozone. Assuming no cloud cover, most long-wave up-welling radiation travels to space through the atmospheric window occurring in the electromagnetic wavelength region between 8 and 11 m where the atmosphere does not absorb long-wave radiation except for in the small region within this between 9.6 and 9.8 m. The interaction between up-welling long wave radiation and the atmosphere is complicated due to absorption occurring at all levels of the atmosphere and this absorption depends on the absorptivities of the constituents of the atmosphere at a particular point in time.

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