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Moderator Performance for Stationary and Rotating Target STS

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					STS04-41-TR0001-R00




Moderator
Performance for
Stationary and Rotating
Target STS
Arrangements




Franz X. Gallmeier




August 2009
This report was prepared as an account of work sponsored by an agency of
the United States government. Neither the United States government nor any
agency thereof, nor any of their employees, makes any warranty, express or
implied, or assumes any legal liability or responsibility for the accuracy,
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by the United States government or any agency thereof. The views and
opinions of authors expressed herein do not necessarily state or reflect those
of the United States government or any agency thereof.
                                                            STS04-41-TR0001-R00



MODERATOR PERFORMANCE FOR STATIONARY AND ROTATING TARGET STS
                      ARRANGEMENTS




                           Franz X. Gallmeier




                      Date Published: August 2009




                            Prepared for the
                       U.S. Department of Energy
                            Office of Science




                Prepared by Oak Ridge National Laboratory
                                   for

                         UT-BATTELLE, LLC
                  under contract DE-AC05-00OR22725
                                 for the
                   U.S. DEPARTMENT OF ENERGY
 Title: Moderator Performance for Stationary and Rotating Target STS Arrangements           Page iii of 22
 ID: STS04-41-TR0001-R00               Author: F. X. Gallmeier              Reviewer: P. D. Ferguson



                                                    TABLE OF CONTENTS


                                                                                                                                         Page

1.    Introduction ............................................................................................................................ 1

2.    Models Description ................................................................................................................ 1

3.    Moderator Performance Calculations .................................................................................... 3

4.    Data Fitting ............................................................................................................................ 6

5.    Fitting Results ........................................................................................................................ 8

6.    Conclusions .......................................................................................................................... 10

7.    References ............................................................................................................................ 10




                                                                     iii
 Title: Moderator Performance for Stationary and Rotating Target STS Arrangements           Page iv of 22
 ID: STS04-41-TR0001-R00               Author: F. X. Gallmeier              Reviewer: P. D. Ferguson



                                                         LIST OF FIGURES

Figure                                                                                                                                    Page

Figure 1.      Target, moderator, reflector assembly (TMRA) of a second SNS target station based
               on a liquid mercury target. ..................................................................................................... 2

Figure 2.      Target, moderator, reflector assembly (TMRA) of a second SNS target station based
               on a rotating tungsten target. ................................................................................................. 3

Figure 3.      Short-pulse emission time distribution of one pulse from the STS2 moderator placed
               on top of a liquid mercury target run at 1 MW at 20 Hz repetition rate.......................... 5

Figure 4.      Long-pulse emission time distribution of one pulse from the STS2 moderator placed
               on top of a liquid mercury target run at 1 MW at 20 Hz repetition rate with 1ms
               proton pulse length..The iteration step of one round of optimization... ................................. 5

Figure 5.      Time-averaged neutron brightness of the face of the cylindrical para-hydrogen
               moderator fed by neutrons from a rotating tungsten target comparing MCNPX
               calculated and a fit to equation (6)... .................................................................................. 11

Figure 6.      Energy-dependent pulse shape parameters α(E), β(E), R(E), and to(E) and their fits to
               generalized Padè functions for the moderator on the liquid mercury target. ................ 12

Figure 7.      Energy-dependent pulse shape parameters α(E), β(E), R(E), and to(E) and their fits to
               generalized Padè functions for the moderator on the rotating tungsten target.. ........... 13

Figure 8. Short-pulse emission time distributions at selected energies for the modetator at the
          rotating tungsten target.. ..............................................................................................14

Figure 9.      Long-pulse (T=1ms) emission time distributions at selected energies for the
               moderator at the rotating tungsten target.. ......................................................................... 15




                                                                      iv
 Title: Moderator Performance for Stationary and Rotating Target STS Arrangements           Page v of 22
 ID: STS04-41-TR0001-R00               Author: F. X. Gallmeier              Reviewer: P. D. Ferguson


                                             LIST OF TABLES

Table                                                                                                        Page

Table 1     Parameters of the fit of the spectral intensities for para-hydrogen moderators at the
            liquid mercury and rotating tungsten targets to equation (6).. .......................................9

Table 2     Neutron pulse shape parameters for moderator at liquid mercury target. ....................... 9

Table 3     Neutron pulse shape parameters for moderator at rotating tungsten target. ..................9




                                                        v
1.   Introduction

     Working towards a design of a second SNS target station tailored to deliver high-intensity cold
     neutron beams to complement the first target station’s high-resolution beams, the most promising
     target-moderator-reflector arrangement (TMRA) using present-day technology has been shown to
     be a large-volume vertical-axis cylindrical liquid para-hydrogen moderator premoderated by a
     mantle of ambient water and viewed by beamlines through three neutron extraction ports[1]. The
     same TMRA concept was applied to a rotating target concept developed by an ORNL LDRD
     program replacing the liquid mercury target with a solid tungsten rotating target disk[2]. Besides
     looking more favorable with respect to the extended target lifetime, this concept also showed
     about 10-15% improved peak-pulse neutron performance[3].

     The present work builds on both the optimized original TMRA and the rotating-target TMRA
     concepts, and performs analyses of extended moderator performance characteristics similar to the
     report by Erik Iverson for the moderator suite of the first SNS target station[4].

     Besides providing data files of spectral intensities and emission time distributions originating
     directly from Monte Carlo simulations, the report also documents an effort of fitting these pieces
     of information to physics motivated functions. The goal was to arrive at complete analytical
     descriptions that may better serve instrument design simulations.


2.   Models Description

     Both concepts build on the cylindrical moderator configuration as defined in reference 1.

     Figures 1 and 2 show three cuts through the wing moderator geometry for the stationary and
     rotating target configurations, respectively. The basic configuration consists of a cylindrical para-
     hydrogen moderator volume surrounded by a layer of light-water pre-moderator all encased
     within a moderator vessel and being viewed by neutron flight channels from the two sides with
     regard to the proton flight direction. The neutron flight channels are 120 mm high and have an
     opening angle in the horizontal set to 36 degrees for the side with regard to the proton beam that
     serves one channel and 24 degrees for both channels on the opposite side; the viewed moderator
     segment is defined such that a 120x100 mm2 area of the moderator can be viewed from all
     directions within the respective channel. Aluminum alloy Al6061 was chosen for all moderator
     and pre-moderator structures with 2 mm wall thickness for the hydrogen and pre-moderator
     vessels, and 4 mm for the moderator assembly container enclosing all moderator and pre-
     moderator components. Also vacuum zones were included for insulation varying from 3 to 5 mm
     thickness. An engineering design of such a moderator structure has not been completed and these
     dimensions are only assumptions.

     For the liquid mercury target based TMRA, the moderator assembly was placed on top of a flat
     rectangular target arrangement. The proton beam is incident horizontally with a beam cross-
     sectional area of 140 cm2 (75×187 mm2). The target height and width dimensions extend about 20
     mm beyond the proton beam footprint. The target volume is contained in a steel vessel with 4 mm
     thickness, a 2 mm thick helium zone, and a double walled heavy-water cooled steel shell of 8 mm
     total steel thickness and a 3 mm thick coolant zone. A steel shielding block extends the target
     beyond the mercury for an additional 1 meter.

     For the rotating target based TMRA, the moderator assembly was placed on top of a cylindrical
     target arrangement consisting of a 600 mm outer radius and 350 mm inner radius bulk tungsten
     ring with a target height of 70 mm backed inside of 350 mm radius by stainless steel. The
                                                  1
tungsten ring was enclosed by a 10 mm thick steel vessel all around and cooled by a 1.5-mm-
thick heavy water zone between the vessel and tungsten. Additionally a central cooling water gap
of 1.5 mm thickness was integrated with a 5 mm high step-up at 525 mm radius. All
tungsten/water interfaces are protected by 1-mm-thick tantalum cladding. A drive shaft was not
considered in the model.

The target and moderator are embedded in a cylindrical beryllium reflector coaxial with the
moderator volume with cutouts for the proton flight path, the target assembly and the moderator
assembly. Radially and axially the reflector extends 35 cm beyond the outer moderator vessel
extensions. A shell of Al6061 of 4 to 5 mm wall thickness and a void zone of the same dimension
separate the reflector from the other components.



                    Vertical cut

                 Beryllium           H20                                          Horizontal
                                                                                  cut on
                                                                                  mid-plane

                        H2



   protons            Hg

                                                                                  Horizontal
                                                                                  cut through
                                                                                  moderator




Fig. 1: Target, moderator, reflector assembly (TMRA) of a second SNS target station based on a
liquid mercury target.




                                           2
                       Vertical cut

                     Beryllium           H20                                           Horizontal
                                                                                       cut on
                                                                                       mid-plane

                           H2




       protons                               SS
                            W
                                                                                       Horizontal
                                                                                       cut through
                                                                                       moderator



          1.5 mm D20 cooling channels

     Fig. 2: Target, moderator, reflector assembly (TMRA) of a second SNS target station based on a
     rotating tungsten target.


3.   Moderator Performance Calculations

     A long MCNPX[5] calculation was performed with cell based weight window settings acquired
     from a previous shorter calculation in order to obtain detailed energy and time dependent
     brightness spectra, and brightness profiles across the viewed moderator area. The energy and time
     dependent brightness was scored by a point detector tally at 10 meters distance from the
     moderator viewed surface with contributions limited by a 120 mm high and 100 mm wide
     acceptance window at the outer hydrogen vessel boundary and established by a collimator of
     60×50 mm cross sectional opening at halfway distance to the point detector. The time binning
     was influenced by a user supplied TALLYX subroutine such that the moderator emission time
     (time at which the neutrons exit the moderator) was scored rather than the arrival time at the
     detector point. This detector modification is known in literature under the name time-of-flight-
     corrected point detector[6]. The transport analyses are performed with proton delta pulses on
     target (short-pulse mode). For energy and time resolution 20 bins per decade from 10-5 to 100 eV
     and from 0.1-3000 μs with constant logarithmic width were considered.

     While this procedure is a good approximation for obtaining neutron responses in the short-pulse
     mode (the neutron moderation time is much longer than the proton pulse width), the proton pulse-
     width has to be folded into the brightness response for the cases with long-pulse mode. While this
     could in principle be achieved by applying a broadened proton pulse in the source definition of
     the transport calculation (long-pulse mode), it was thought to be more efficient to use the
     moderator performance data obtained in short-pulse mode and fold it with the proton pulse time
     structure externally.


                                                  3
For the long-pulse case, the proton pulse distribution broaden the neutron emission time
distributions ilp(E,t) by folding the proton pulse distribuation with the short-pulse neutron
emission time distributions isp(E,t)
                         t
        ilp ( E , t )   isp ( E, t   ) P( )d                         (1)
                         0


The proton pulse distribution P(t) is assumed as a step function of time
               1 / T ;   t T
       P(t )                                                             (2)
                0; t  0  t  T
which simplifies equation (1) to

                             T min
                         1
        ilp ( E, t ) 
                         T    i
                              0
                                   sp   ( E, t   )d                     (3)

with
        Tmin  min (T , t )                                                (4)

This is done in a post-processing step arriving at moderator brightness data files for the short-
pulse mode in the energy and time structure of the MCNPX tallies and for the long-pulse modes
in a time structure of constant bin width. These data files are provided as source descriptions for
neutron instrument optimization calculations. The resulting short and long pulse neutron emission
time distributions are presented in overview plots in Figs. 3 and 4 for the stationary mercury
target case.

All data are normalized to 1MW proton beam on target with a proton energy of 1.3 GeV and a
pulse repetition rate of 20 Hz.




                                                         4
Fig. 3: Short-pulse emission time distribution of one pulse from the STS moderator
placed on top of a liquid mercury target run at 1 MW at 20 Hz repetition rate.




Fig. 4: Long-pulse emission time distribution of one pulse from the STS moderator
placed on top of a liquid mercury target run at 1 MW at 20 Hz repetition rate with 1ms
proton pulse length.



                                        5
4.   Data Fitting

     The neutron emission time distributions were fitted to suitable analytic functions in three fitting
     campaigns:

            Fitting of the spectral intensities (time integrated emission time distributions) to coupled
             modified Maxwellian and epithermal spectral dependence;

            Fitting of array of time distributions to slowing down and thermalization functions for
             each energy bin arriving at pulse shape parameters for each energy bin;

            Fitting of pulse shape fitting parameters to energy dependent generalized Padè functions.

     While the first two fitting processes are physics inspired, the last step is purely mathematical and
     motivated by the desire of obtaining a complete analytical representation of the emission time
     distributions. The fitting of the short-pulse representation will also yield an analytical expression
     for the long-pulse representation by applying the folding of equation (3) on the short-pulse
     functions analytically. The basis and physics behind the fitting functions are developed and
     summarized in a paper draft[7] provided to us by J. M. Carpenter.

     The first fitting step acts on the short-pulse spectral intensity Isp(E) defined as the integral over
     time of short-pulse neutron emission time distributions isp(E,t):

                          
             I sp ( E )   isp ( E , t )dt
                          0                                                               (5)

     The fitting function consists of a slowing-down spectrum and three Maxwellian terms with the
     highest energy Maxwellian allowing a variable power exponent:

                                                   E           E             E       E 
               I sp ( E )  I epi exp(c / E ) R1      2       kT   R2 (k T ) 2 exp  kT 
                                                          exp                                 
                                               (k T1 )              1         2             2 
                                                                                                      (6)
                                                             E              E b  ( E )  ( E ) 
                                                    R3           2      kT )   E (1 a ) 
                                                                    exp  (     
                                                          (k T3 )            3                  

     The epithermal and Maxwellian components are joined by the generalized Westcott function
     introducing the parameters Ecut and exponent s

                               1
             ( E )                   s
                            E 
                        1   cut 
                             E                  .                                       (7)

     Brun’s modification factor ρ(E) is an approach[8] to take into account the large drop of the para-
     hydrogen cross section at the dominant rotational excitation

                                                 x2 
              ( E )  1   exp( x)1  x 
                                                    
                                                 2                                     (8)
                                                      6
with

                  ( E  2 B)             for E  2 B
        x( E )  
                       0                  for E  2 B                                     (9)

where B is the free H2 rotational constant (B=7.36 meV).

For fitting the emission time distributions, a slowing-down function coupled to a storage term
were considered well known as Ikeda-Carpenter function f(E,t) with the four energy-dependent fit
parameters α(E), β(E), R(E), and to(E) [9]):

                                                                          3
           f ( E, t ' )         1  R t '2 exp t '  R                   
                             2                                          (   ) 3
                                                                  1                 
                     exp( t ' )  exp(t ' ) 1  (   )t '  (   ) 2 t ' 2 
                                                                  2                    (10)

with

        t'  t  to
                                            .                                              (11)

The emission time distributions isp(E,t) can be written as a product of the spectral intensity Isp(E)
and pulse shape functions fsp(E,t):

        i sp ( E , t )  I sp ( E ) f sp ( E , t )
                                                                                           (12)

Since the Ikeda Carpenter function is normalized such that the time integral at any energy E
returns unity, it is well suited for fitting the pulse shape functions fsp(E,t).

Equations (3) and (4) can be transformed by t’=t-τ to

                             t
                          1                          I sp ( E ) t
        ilp ( E , t )        isp ( E , t ' )dt ' 
                          T Tmin                         T Tmin  f sp ( E, t ' )dt '
                                                                                           (3’)

with

                0                for t  T
        Tmin  
               t  T             for t  T                                                (4’)

Equation (3’) can formally be integrated using (10) arriving at




                                                            7
               F ( E , t" ) 
                                 1 1  R 1  t" t"2  exp t"  R
                                                              
                                                                                         3
                                                                                                 
                                                                            
                                  T 
                                                                   2               (   ) 3
                                               (   )              (   ) 2             t"2     
         exp( t" )  exp(t" )             1        (1  t" )                1  t"            
                                                                        2                            
          
                                                                                               2        
                                                                                                                (13)

     and

             ilp ( E , t ' )  I sp ( E ) F ( E , t ' )  F ( E , Tm in )
                                                                                                     (14)

     and

             t'  t  to
                                                                                                     (15)

     The energy-dependent parameters α(E), β(E), and to(E) are fit to generalized Padè function

                                  1  CE  DE 2  E / F 
                                                                     G
             y( E )  AE      B

                                  1  HE  JE 2  E / K 
                                                                     L
                                                                                  ,                  (16)

     where a simplified version with B=0 and G=L was used for the parameter R(E).


5.   Fitting Results

     The fitting parameters of the spectral intensities obtained for the large para-hydrogen moderator
     fed by the liquid mercury and rotating target are listed in Table 1. The fit agrees well with the
     simulation results as demonstrated in Fig. 5 for the moderator at the rotating tungsten target. The
     discontinuity in the spectrum at about 0.4 eV in the simulation results is the result of the change
     between the scattering kernel and the ENDF/B cross section treatment in MCNPX and is removed
     by the fitting result.

     The parameters A, B, C, D, F, G, H, J, K L for the Padè functions of the pulse shape parameters
     α(E), β(E), and to(E) are listed in Table 2 and 3 for the moderator at the liquid mercury and
     rotating tungsten targets, respectively. Figs. 6 and 7 document the pulse shape parameters as
     calculated for each energy bin and the respective Padè function fits for moderators both at the
     liquid mercury target and rotating tungsten target configurations. It becomes apparent that the
     Padè functions have problems in describing depressions in the parameter settings around 0.01 eV.
     This is not so much a deficit of the Padè but has deeper roots. Comparing the emission time
     distributions as obtained from the simulations to Ikeda-Carpenter function fits reveal that the
     Ikeda-Carpenter functions are not well suited as fitting functions in the energy range from 0.7 to
     15 meV, while they work reasonably well below 0.7 meV and above 15 meV as shown in Fig. 8.
     In this particular range, the pulse shape is broadened possibly by complex thermalization
     processes of neutrons below 20 meV traveling repeatedly across the moderator volume due to
     large large mean free paths and having repeated interaction with the ambient water pre-
     moderator. In the long-pulse mode, these effects are largely smeared out as shown in Fig. 9,
     which presents the long-pulse emission time distributions for the exact same energies as shown in
     Fig. 8 for short-pulse distributions.

                                                                8
Table 1: Parameters of the fit of the spectral intensities for para-hydrogen moderators at
the liquid mercury and rotating tungsten targets to equation (6).
                                   Cylindrical para hydrogen moderator
 Fit parameter
                                   @ liquid mercury target       @ rotating tungsten target
 Iepi (1012 n/sterad/eV/pulse)               1.5929                        1.7485
 c (√eV)                                   0.001348                      0.001849
 R1                                           5.516                         5.199
 T1 (K)                                       20.22                         20.06
 R2                                           5.379                         4.886
 T2 (K)                                       74.03                         76.32
 R3                                           29.06                         27.79
 T3 (K)                                      121.06                        119.84
 A                                          0.01468                       0.01927
 B                                           2.4648                        2.3991
 Ecut (eV)                                    0.025                         0.025
 S                                           1.2728                        1.1851
 γ (1/eV)                                     46.46                         44.90
 Δ                                           0.7698                        0.6683

Table 2: Neutron pulse shape parameters for moderator at liquid mercury target.
                                     Pulse shape Parameters
 Padè Parameters
                    α            β              R               to
         A          0.05185      0.0035198      0.90179         1.5542
         B          0.11765      0.070061       0               -0.18021
         C          243.04       -3.1885        -21.517         -19504.5
         D          18800.1      20279.0        6.5389          564.79
         F          0.012557     0.037421       0.052069        7.4181
         G          7.4117       6.0884         1.0412          1.2081
         H          -31.256      -79.769        13.635          -10036.2
         J          19479.7      15903.4        74.650          72.216
         K          0.015467     0.055332       9.5963          0.000096762
         L          7.0559       5.6990         1.0412          1.5509

Table 3: Neutron pulse shape parameters for moderator at rotating tungsten target
                                     Pulse shape Parameters
 Padè Parameter
                    α             β             R               to
         A          0.00048406 0.0043308 0.89999                0.052377
         B          -0.32904      0.083279      0               -0.50402
         C          4.7676        247.52        -52.423         -11279.5
         D          132.48        -6720.4       6.1913          4630.1
         F          0.00018878 0.021877         0.02073         0.00012015
         G          0.92771       2.6745        1.02455         1.2319
         H          -0.067293     94.2222       12.064          -2495.4
         J          0.00087482 -2876.2          126.45          2301.3
         K          3.7019        0.022748      7.6568          0.00019390
         L          0.81381       2.1748        1.02455         1.2522
                                       9
     An in depth study of the neutron moderation and thermalization dynamics in the complex para-
     hydrogen, ambient water and beryllium reflector is needed to come up with better pulse shape
     functions of the considered systems.


6.   Conclusions

     Moderator performance data in the form of spectral intensities and neutron emission time
     distributions for coupled pre-moderated cylindrical large-volume para-hydorgen moderators at a
     stationary liquid mercury target and at a rotating tungsten target were obtained from larger scale
     Monte-Carle simulations of infinitely narrow proton pulses incident on the targets applying the
     MCNPX code.

     These data were prepared as short-pulse and long-pulse data sets to be input to neutron optics and
     instrument simulations.

     Some effort went into fitting the spectral intensities and emission time distributions to arrive at
     closed analytic expressions that would allow for a more compact and more flexible description of
     moderator performance. While the spectral intensities were easily fit to physically inspired
     coupled slowing-down and thermalization functions, the use of Ikeda-Carpenter functions for the
     description of the emission time distributions was not fully convincing. Parahydrogen coupled to
     water pre-moderator and beryllium reflector seems to be a fairly complex system in terms of
     neutron moderations. For the long-pulse representation of the pulse shapes, most of the pulse-
     shape ambiguities smear out such that the resulting analytical representation of the emission time
     distribution constitutes an alternative to the simulation data files for instrument simulations.



7.   References
     [1] F. X. Gallmeier, Moderator Performance for Stationary and Rotating Target STS2
     Arrangements, SNS 00000000-0000-R00, ORNL, January 2009.
     [2] T. McManamy et al, 3 MW Solid Rotating Target Design, Ninth International
         Workshop on Spallation Materials Technology (IWSMT9), Hokkaido University,
         Sapporo. Japan, October 19-24, 2008.
     [3] F. X. Gallmeier, Neutronics Analyses in Support of the SNS Rotating Target
     LDRD Project, SNS 00000000-0000-R00, ORNL, May 2009.
     [4] Iverson E.B. et al, Detailed SNS Neutronics Calculations for Scattering Instrument Design:
     SCT Configuration, SNS-1100403300-DA0001-R00, Oak Ridge National Laboratory, Oak
     Ridge, July 2002.
     [5] Pelowitz D. B., editor, MCNPX User’s Manual Version 2.5.0, LA-CP-05-0369, Los Alamos
     National Laboratory, Los Alamos, April 2005 (also see http://mcnpx.lanl.gov).
     [6] Micklich B. J, and Iverson E. B., Calculation of pulse shapes for reentrant moderators,
     Nuclear Mathematical and Computational Sciences: A Century in Review, A Century Anew
     Gatlinburg (MC2003), Tennessee, April 6-11, 2003, on CD-ROM, American Nuclear Society,
     LaGrange Park, IL (2003)
     [7] Carpenter J. M. et al., Methods for Characterizing Pulsed-Source Moderators, a draft report,
     2009.
     [8] T. O. Brun, “Spectra and pulse shapes of a decoupled liquid hydrogen moderator,” in
     Proceedings of the International Workshop on Cold Moderators for Pulsed Neutron Sources (J.
     M. Carpenter and E. B. Iverson, eds.), pp. 163–170, OECD, 1998.
     [9] S. Ikeda and J. M. Carpenter, Nucl. Instrum. Methods A239, 536 (1985).

                                                10
Fig. 5: Time-averaged neutron brightness of the face of the cylindrical para-hydrogen moderator
fed by neutrons from a rotating tungsten target. The graph compares MCNPX calculated
brightness values to a least square fit to equation (6).




                                              11
Fig. 6: Energy-dependent pulse shape parameters α(E), β(E), R(E), and to(E) and their fits to
generalized Padè functions for the moderator on the liquid mercury target.




                                               12
Fig. 7: Energy-dependent pulse shape parameters α(E), β(E), R(E), and to(E) and their fits to
generalized Padè functions for the moderator on the rotating tungsten target.




                                               13
Fig. 8: Short-pulse emission time distributions at selected energies for the modetator at the
rotating tungsten target.




                                                14
Fig. 9: Long-pulse (T=1ms) emission time distributions at selected energies for the moderator at
the rotating tungsten target.




                                               15
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