Reactivity

When a nuclear power-reactor plant is generating electrical energv at a steadv or constant rate, the reactor is in a steady state m which the neutron density is fixed, the temperatures at various positions in the reactor are con­stant, etc Equations 1 7 and 1 8 show that, since dn/dt = dC,/dt = 0 in this steady state, the effective multi­plication factor is just 1 If the effective multiplication factor increases above 1, n will increase with time Similarly, when к < 1, n decreases with time

s к is increased above 1, it reaches a value where the first term of Eq 17 becomes zero, then, for higher values of k, the term becomes positive When k(l — (3) — 1 is positive, the neutron density increases with time at a rate depending on the ratio of the prompt-neutron lifetime, /, to k(l — (3) — 1 Under these conditions the reactor is prompt critical, and, because / is so small (/ ^ 10 4 sec for a thermal reactor, / A? 10 7 sec for a fast reactor), n increases very rapidlv with time for anv appreciable positive value of k( 1 — /3) — 1 The value of the effective multiplication factor when the reactor is just prompt critical is 1/(1 — (3) Since power reactors are always kept below prompt criticality, the practical range of the effective multiplication factor is between 1 and 1/(1 —/3) when the reactor is operating and between 0 and 1 when the reactor is being started up or shut down

In place of the effective multiplication factor it is more convenient to refer to the reactivity, or the fractional deviation of the effective multiplication factor from unity, (k — l)/k,

к — 1 5k, ,

Reactivitv = p = —:— = — (19)

к к

When the effective multiplication factor varies from 1 to 1/(1 — 13), the reactivity varies from 0 to /3 In other words, the reactivity increases by (3 as the reactor goes from delayed critical to prompt critical It is convenient to designate this change of reactivity as “one dollar” = $1 = unit of reactivity equal to the reactivity difference between the prompt critical (k = 1/1 — (3) and the delayed critical (k = 1) conditions of a reactor The dollar is further subdivided into 100 cents, a change in reactivity of 1$, for example, is Др = 0 01/3 from the values of (3 in I able 1 3, it follows that a l<f reactivity increment is 0 000064 for a 2 3 5 U-fueled reactor

frequently the terms “excess k,” “5k/k,” and “reac tivity ” are used interchangeably As fq 19 shows, the second and third terms are exactly equivalent 1 he use of “excess k” or “5k” as equivalent to reactivity is approxi­mately correct, since p = 5k/k = 5k/(l + 5k) = 5k — (5k)2 , etc, and 5k < 1 in all practical cases

Table 1 2—Delayed-Neutron Half-Lives and Yields in hast I ission*7

Delayed Group Relative Absolute

Isotope

neutrons/

fission

index

(0

Half-life <T^>, see

Decay constant

(X), sec 1

abundance

(a)

group yield,

%

33u

0 0070 4 0 0004

і

55 11 +

1 86

0 0126 4 0 0004

0 086

4 0 003

0 06 4

0 003

2

20 74 +

0 86

0 0334 4 0 0014

0 274

4 0 005

0 192 ±

0 009

3

5 30 4

0 19

0 131 + 0005

0 227

4 0 03 5

0 159 4

0 025

4

2 29 4

0 18

0 302 4 0 024

0 317

4 0 011

0 222 ±

0 012

5

0 546 +

0 108

1 27 4 0 266

0 073

4 0 014

0 051 4

0 010

6

0 221 +

0 042

3 13 4 0 675

0 023

± 0 007

0 016 4

0 005

2 3 5 и

0 0165 ± 0 0005

1

54 51 4

0 94

0 0127 + 0 0002

0 038

4 0 003

0 063 4

0 005

2

21 84 +

0 54

0 0317 00008

0 213

4 0 005

0 3 51 ±

0 Oil

3

6 00 4

0 17

0 11 5 4 0 003

0 188

4 0 016

0 310 4

0 028

4

2 23 ±

0 06

0 311 4 0 008

0 407

+ 0 007

0 672 ±

0 023

5

0 496 4

0 029

1 40 4 0 081

0 128

4 0 008

0 211 4

0 015

6

0 179 4

0 017

3 87 4 0 369

0 026

4 0 003

0 043 4

0 005

2 3 8 U

0 0412 4 0 001 7

1

52 38 +

1 29

0 01 32 4 0 0003

0 013

4 0 001

0 054 4

0 005

2

21 58 +

0 39

0 0321 4 0 0006

0 137

+ 0 002

0 564 ±

0 025

3

5 00 4

0 19

0 139 0 005

0 162

4 0 020

0 667 ±

0 087

4

1 93 ±

0 07

0 3 58 0 014

0 388

4 0 012

1 599 4

0 081

5

0 49 +

0 023

1 41 4 0 067

0 225

4 0 013

0 927 4

0 060

6

0 172 +

0 009

4 02 4 0 214

0 075

+ 0 005

0 309 4

0 024

2 3 9 l’u

0 0063 + 0 0003

1

53 75 4

0 95

0 0129 ± 0 0002

0 03 8

4 0 003

0 024 4

0 002

2

22 29 ±

0 36

0 0311 4 0 0005

0 280

4 0 004

0 176 ±

0 009

3

5 19 4

0 12

0 134 4 0 003

0 216

4 0 018

0 136 ±

0 013

4

2 09 4

0 08

0 331 4 0 012

0 3 28

4 0 010

0 207 4

0 012

5

0 549 4

0 049

1 26 4 0 115

0 103

+ 0 009

0 065 ±

0 007

6

0 216 +

0 017

3 21 0 255

0 03 5

+ 0 005

0 022 4

0 003

2 4 0 Pu

0 0088 + 0 0006

1

53 56 4

1 21

0 0129 4 0 0004

0 028

4 0 003

0 022 +

0 003

2

22 14

0 38

0 0313 4 0 0005

0 273

4 0 004

0 238 ±

0 016

3

5 14 4

0 42

0 135 4 0 011

0 192

4 0053

0 162 ±

0 044

4

2 08 4

0 19

0 333 + 0 031

0 3 50

4 0 020

0 315 4

0 027

5

0 511 4

0 077

1 36 + 0 205

0 128

4 0 018

0 119 4

0 018

6

0 172

0 033

4 04 4 0 782

0 029

4 0 006

0 024 ±

0 005

2 3 2 1 h

0 0496 + 0 0020

1

56 03 4

0 95

0 0124 0 0002

0 034

0 002

0 169 4

0 012

2

20 75 4

0 66

0 0334 0 0011

0 150

4 0 005

0 744

0 037

3

5 74 4

0 24

0 1 21 4 0 005

0 155

4 0 021

0 769 4

0 108

4

2 16 4

0 08

0 321 4 0 01 1

0 446

0 015

2 212 4

0 110

5

0 571 4

0 042

1 21 + 0 090

0 172

4 0 013

0 853 4

0 073

6

0 211

0 019

3 29 4 0 297

0 043

4 0 006

0 213 4

0 031

* bast fission is defined as fission induced by a continuous neutron spectrum similar to a prompt fission neutron spectrum

Tabic 1 3—Delayed-Neutron Fractions and Yields* +

Fission

nuclide

(Eeff

Fast fission ~ fission spectrum)

Thermal neutron induced fission

n/1

V

0

n/F

V

/3

2 3 9 pu

0 0063 0 0003

3 08 4

0 04

0 0020,

± 0 0001,

0 0061 4 0 0003

2 82„

0 02,

0 0021, 4

0 0001,

2 3 3 u

0 0070 4 0 0004

2 61 4

0 03

0 0026„

4 0 00016

0 0066 4 0 0003

2 46, 4

0 020

0 0026, 4

0 0001,

2 4 0 Pu

0 0088 4 0 0006

3 3 4

0 2

0 00266

4 0 0002,

241 Pu

0 0154 4 0 0015

3 14 4

0 06

0 0049 4

0 0005

2 3 3 U

0 0165 4 0 0005

2 59 4

0 03

0 0063,

+ 0 00022

0 0158 4 0 0005

2 43„ 4

0 001

0 0065„ ±

0 0002,

4 3 8 u

0 0412 + 0 001

2 80 >

0 13

0 0147

4 0 0009

2 3 2 Th

0 0496 0 0020

2 42

0 20

0 0205

4 0 0019

*From

H C Paxton and

C, R

Kecpin

Tin Technology of

Nuclear Reactor Safety Vol

1 P

267 The M I

1 Press

Cambridge Mass 1964

tSymbols n/b = delayed neutrons per fission v = average total neutrons per fission 0 = n/I v = fraction of total neutrons that arc delayed

Подпись: TkПодпись: 2 ;= і Подпись: PПодпись: (1.13)

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