Marginally Trapped Neutrons. Kevin Coakley National Institute of Standards and Technology Boulder, Colorado

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1 Marginally Trapped Neutrons Kevin Coakley National Institute of Standards and Technology Boulder, Colorado Presentation for workshop on Next Generation Neutron Lifetime Experiments, Sane Fe, NM. November 9-1,

2 Outline General remarks. Analysis of marginally trapped neutrons in NIST magnetic trapping experiment. Modeling assumptions Systematic error 2

3 General comments For a static potential, a neutron with energy E is marginally trapped if E > V min where V min is the minimum potential energy on the trap boundary. If losses due to β decay, marginally trapping, and other mechanisms are independently, the survival probability of a neutron is where Observed β decay signal S(t) = S β (t)s M (t)s other (t) S β (t) = exp( t τ n ). r β = < N() > S M (t)s other (t) exp( t ). τ n τ n 3

4 Non-exponential survival probability If derivative of ln S(t) varies with time, S(t) is not exponential. Given Ṡ(t) S(t) = 1 τ(t), S(t) = exp( Z t s= ds τ(s) ). 4

5 Craig Huffer P. Huffman K. Schelhammer D. Marley A. Yue C. O Shaughnessy P. Hughes HP. Mumm M. Huber A. Thompson K. Coakley M. Dewey N. Abrams 1 5

6 Superthermal Production 4 n Superfluid Helium ucn phonon ~.95 mev (12 K or.89 nm) neutrons can scatter in liquid helium to near rest by emission of a single phonon. Upscattering (by absorption of an 12 K phonon)! Population of 12 K phonons ~ e! 12 K T bath p Energy ( /k B in K) UCN = n Ð p phonon E UCN p = E n Ð E phonon p 2 2m Elementary Excitations in Liquid Helium Golub and Pendlebury, Phys. Lett. 53A (1975), p Momentum Q ( in nm -1 ) h 6

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8 Solenoids Quadrupole Beam On Beam Off 43 8

9 Marginally Trapped Neutrons 48 There are neutron orbits where E tot = E kin + B r B 1/3 = const.3 B Briefly ramping the magnetic field down to.3 B and back up eliminates most neutrons on these orbits, but also reduces the number of trapped neutrons. 9

10 Tracking Ultra Cold Neutrons (UCN) V = µ n B solenoid + B quadrupole Tensor spline model for B-fields Symplectic integration to predict trajectories Initial UCN positions in trap are uniform, initial velocity distribution f(v) v 2. More details: Coakley et. al, J. Res. Natl. Inst. Stand. Technol. 11, (25). 1

11 x (cm) y (cm) z (cm) time (s) time (s) time (s) v x (cm/s) v y (cm/s) v z (cm/s) time (s) time (s) time (s) 11

12 Neutron Wall Interactions Reflection probability model based on nuclear potential models multilayer model for cylindrical surface homogenous material at endcaps surface roughness not explicitly modeled Lambertian diffuse reflection model Ongoing Sensitivity studies BN dust particles assumed parameter values in scattering potential models 12

13 Wall effects : Golub et al Above threshold neutrons hitting the wall have non-zero reflection probability. V = VTPB VHe 42 nev - 2 nev = 22 nev W = 1 3 nev 13

14 1 TPB/Gortex Graphite BN He TPB PTFE Graphite BN V (nev) Loss Probability W (nev) Neutron Energy nev 16 14

15 Loading the trap with UCN Production of UCN in trap is a Birth-Death Stochastic process (Coakley NIMA 46 (1998) ). Given that loading stage is from to t L, and that the production rates of below and above threshold UCN are λ and λ +, the expected number of above and below threshold UCN at time t L are and < N + (t L ) >= λ + Z tl s= < N (t L ) >= λ Z tl S other (t L s)s M (t L s) exp( t L s )ds τ n s= S other (t L s) exp( t L s )ds τ n If S other = 1, < N (t L ) >= λ τ n (1 exp( t L τ n )). 15

16 1 Survival probablity of UCN in static and ramped (.7 to.35 to.7) trap survival probabilty after 56 s static trap ramped trap (above threshold) ramped trap (below threshold) threshold energy (nev) 16

17 Monte Carlo estimate of survival probability (± s.e. bands) for Marginal Trap loss mechanism 1.9 estimated survival probabilty S M (t) time after creation (s) 17

18 Monte Carlo estimate of survival probability (± s.e. bands) for Marginal Trap loss mechanism 1.9 estimated survival probabilty S M (t) time after creation (s) 18

19 1.95 S + M (t) T L s= exp((s T L)/τ n )S M (t s)ds estimate end observation (t) after loading trap normalized S + M time after trap is loaded (s) 19

20 Observed β decay signal after loading trap: t L t t end. r β = f + f c f = < N (t L ) > + < N + (t L ) > S + M (t end) τ n exp( t t L τ n ) f c = < N +(t L ) > ( S + M (t) S+ M (t end) ) τ n exp( t t L τ n ) Contamination ratio. r c (t) = f c f 2

21 1 6 simulation static trap observed contamination due to marginally trapped neutrons neutron decay signal of interest counts time after loading (s) 21

22 .25 static trap.7 of maximum current ramped trap:.7 to.5 to.7 ramped trap: contamination ratio r c time after fill (s) 22

23 case estimated systematic error standard error static - 58 s 6 s ramp s 2 s ramp s.9 s Table 1: Monte Carlo estimation of systematic error due to contamination by marginal trapped neutron. The quadrupole field is ramped but not the solenoid field. Assumed value of τ n is 886 s. Sensitivity studies related to modeling assumputions are ongoing. 23