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NUCLEAR PHYSICSANDREACTOR THEORYA one-hour overview

RADIOACTIVITY

Nuclear instability

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TYPES OF RADIATION

NUCLEAR STABILITY CURVE

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BINDING ENERGY

FISSION

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ACTUAL FISSION

FISSION

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FISSION PRODUCT YIELD

FISSION PRODUCTSVARY WITH FUEL TYPE

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CHAIN REACTION

NEUTRONLIFE-CYCLE

Multiplication Factork ≡ neutrons in this generation divided by k ≡ neutrons in this generation divided by

number of neutrons in previous generation

“Four – Factor” Formulak = ε•p•f•ηk∞ = ε•p•f•η

“Six – Factor” Formulakeff = ε•Lf•p•Lt•f•η

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NEUTRON LIFE-CYCLE

keff = ε•Lf•p•Lt•f•η

Term Range Typical

Fast Fission Factor (ε) > 1.0 1.04Fast Non-leakage Probability (Lf) < 1.0 0.86Resonance Escape Probability (p) < 1.0 0.49Thermal Non-leakage Probability (Lt) < 1.0 0.84Thermal Utilization (f) < 1.0 0.90Neutron Production Factor (η) > 1.0 2.65

NEUTRON LIFE-CYCLE

Fission Production of Fast Neutrons (η)

Ni = N0ηN i+1= NiηεLfp Ltf

Fast Fission Factor (ε)

Ni = N0ηεNi = N0ηεLfp Lt

Thermal Utilization

(f)

Keff=Ni+1/Ni

Keff=ηεLfp Ltf

Fast Non-leakage

(Lf )

Ni = N0ηεLfResonance Escape

Probability (p)

Ni = N0ηεLfpLf p

Thermal Non-Leakage

(Lt)

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CORE DESIGN

keff = ε•Lf•p•Lt•f•η

Minimize LeakageLf•p•Lt

Maximize Use and Production

ε•f•ηε•f•η

By varyingGeometryCore Contents

NUCLEAR CROSS SECTIONS(1 BARN = 1 E-24 CM2

R=σNφ

1/v region

Approximate Energy of Thermal Neutrons

Resonance Absorption Peaks

fission production

region

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THERMALIZATION OF NEUTRONS

FUEL DESIGN ANDCORE DESIGN

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CORE GEOMETRY AND MASS FRACTIONS

Fuel Pin Pitch

Water Gap

Fuel Pins

Instrumentation

Control Rodor

Water Channel

MODERATOR TEMPERATURE COEFFICIENT

ter) Negative FeedbackPositive Feedback

R ti itactio

n M

oder

ator

(Wat

Area of Operation

Reactivity

Fra

Temperature

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REACTIVITY

The number of neutrons present in the core after a given number of generations isgiven number of generations is

Nn = No (keff)Reactivity is the fractional change in neutron

population per generation.Reactivity is then:

ρ = (k ff-1)/k ffρ = (keff-1)/keffand

keff= 1/(1-ρ)

POWER CHANGES

Reactor Power = F(prompt neutrons) + F(delayed neutrons)F(delayed neutrons)

(in 235U, β = 0.007)

Typically 6 groups of delayed neutrons are modeledfrom fission product decay processes that emits neutrons (arbitrarily arranged into 6 groups of similar decay rate) – referred to as precursors

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POWER CHANGES

By observation, power changes follow the sum of exponential curves, i.e.exponential curves, i.e.

P(t) = P0ekot + Σβi(0)ekit + other stuff

REACTOR DYNAMICS

Inhour Equation

(where power will be in an hour)

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INHOUR SOLUTIONS(IF ANYONE CARES….)

POWER INCREASE

Steady Exponential Increase

Ln(P

ower

)

Initial Power

Prompt Jump

Time

Proportional to Reactivity ‘added’

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POWER DECREASE

Initial PowerInitial PowerPrompt Drop

Steady Exponential DecreaseLn

(Pow

er)

Proportional to Negative Reactivity

Inserted

Time

POWER GENERATIONAFTER A REACTOR TRIP

300

350

7%

8%

100

150

200

250

300

2%

3%

4%

5%

6%

7%

Pow

er (M

Wt)

Pow

er (%

or R

ated

)

0

50

0%

1%

0.1 1 10 100 1000 10000

Seconds after Reactor Trip

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REACTOR DYNAMICS

What mattersAll power changes follow compound exponential All power changes follow compound exponential curves Power never goes to zeroTime to make power level change depends on whether prompt or delayed neutrons are governingAll power reactor operations are in delayed neutron governed regions

QUESTIONS?