STATE RESEARCH CENTER OF RUSSIA

INSTITUTE FOR HIGH ENERGY PHYSICS

RU�������� Protvino� Moscow Region� Russia

NuMI�B�XXX

June ��� ����

Temperature and Stresses in the LE Target

with ��� mm Wide Segments

S�Filippov� V�Garkusha� F�Novoskoltsev� A�Ryabov�V�Zarucheisky

Introduction

The advanced conceptual design of the LE target �the target intendedto be used in the NuMI low energy neutrino beam� is described in ����while ��� gives results of calculations of dynamic stresses induced in thetarget material by the �� �s single turn extracted primary beam� as wellas results of LE target prototyping� which were fabricated to test the generalconstruction technics and that alignment tolerances can be met�

Following a new conception of the bae protection colimators� whichkeeps the focusing system and all decay region from entering of the mis�steered primary proton beam� the width of graphite target segments wasincreased from ��� mm up to � mm at the same proton beam spot size�In response to these changes in a target design this Report presents resultsof temperature and stress calculations showing ���� increase of the safetyfactor� Approximately ��� loss of neutrino events with ��� � E� � �� GeVdue to extra absorption of secondaries in a target material was consideredas acceptable taking into account a few percents increase of neutrino eventswith E� � ��� GeV�

Cross�section of the LE target with � mm wide segments is shown inFigure ���� The target core is a row of � graphite segments� each �� mmhigh and �� mm long� The segments are soldered by means of a soft solderto two steel cooling pipes with external diameter �� mm and wall thickness��� mm� The target core is inserted into a �� mm thick �� mm diameteraluminum casing and centered by �ve � mm thick aluminum spacers�

Energy Deposition in the Target

Calculations of energy deposition were made using the MARS� ������code ��� for the primary proton beam with Gaussian distributions in bothtransverse directions �x � �y � ��� � �� mm��

The energy deposition density at the beam axis reaches the maximalvalue of ������ GeV�cm��proton in � segments and then decreases con�tinuously to ������ GeV�cm��proton at the downstream end of the target�Distributions of average power deposited in the target �Figure ���� are givenfor the primary beam with intensity of ����� protons per ��� s� The powerdeposited in target segments is equal to ��� kW� With addition of �� � kWdeposited in steel pipes and in cooling water� the total load to the watercooling system is about �� kW �Table �����

�

Elements Width of a target segment�of the LE target ��� mm � mm

Graphite segments ���� �����Cooling pipes ����� �����

Cooling water ��� � �����Aluminum casing ����� ��� �

Total ����� �����

Table ���� Energy deposition �kW� in di�erent elements of the LE target�

Cooling of Target Segments

Calculated values of a heat transfer coe�cient� a pressure drop� a �owrate and a temperature rise of a cooling water as functions of a water �owvelocity in the target cooling system are given in Table ���� Calculationswere made for cooling pipes with internal diameter of �� mm and roughnessof ���� mm� Taking into account that the input temperature of a coolingwater is equal to ���C� a relatively wide range of water �ow velocities from� up to m�s is acceptable for cooling of target segments�

Velocity of a cooling water� m�s � �

Heat transfer coe�cient� kW�m��K �� � ��

Pressure drop� atm ���� ��� ���Water �ow rate� l�min ��� �� ���Water temperature rise� �C �� �� ���

Table ���� Main parameters of the LE target cooling system�

Temperature and Stresses in Target Segments

Calculations of target temperature� as well as stresses induced in a targetmaterial by the single turn extracted primary beam with � � �� �s weremade by the ANSYS �Figure ���� under the following boundary conditions�

� the thermo�resistance between target segments and cooling pipes isequal to zero� The input temperature of cooling water is equal to ���C�

� a heat transfer coe�cient to the ambient atmosphere is equal to zero�i�e� the target is in vacuum�

�

� for thermal radiation� target segments have an emissivity of ��� and theambient temperature is ���C�

No prestress of the material was included in stress calculations� Despite ofthe some di�erence in thermal expansion coe�cients of the graphite andcooling pipe steel �� the high plasticity soft solder� used for soldering of tar�get segments to cooling pipes� prevents arising of stresses in graphite duringcooling of the soldered assembly from �����C to the room temperature�

Results of calculations of temperature and stresses in a target segmentwith the highest energy deposition density are given in Figure �� ���� andin Table ���� Comparison of these results with those obtained withoutthermal radiation shows its relatively small in�uence on the steady�statetemperature of a target�

Width of a target segment� mm ��� �

Temperature before beam spill� �C � �� ����

Temperature rise� �C �� ���Temperature after beam spill� �C ��� ���

Max� equivalent stress at the center ofsegment �all�axis compression�� MPa ���� ��� Max� equivalent stress at the roundedcorner of segment �all�axis stretch�� MPa ���� ����

Safety factor ��� ���

Table ���� Temperatures and maximal thermal stresses in target segmentswith the highest energy deposition density�

Since the graphite has di�erent compressive and tensile strength limits�which are equal to ��� MPa and �� MPa respectively for used ZXF��Qgrade with density of ���� g�cm� � �� the crucial point for a target materialintegrity is at the rounded corner of segment where graphite is subjected toall�axis stretch� Taking into account that the high cycle fatigue endurancelimit of graphite is in the range of ������ ���� the safety factor �the ratioof the fatigue endurance limit to the maximal equivalent stress occurringin target segments� is about ����

�Thermal expansion coe�cients of the ZXF��Q graphite and steel used for production of cooling pipesare equal to �������� and ��������� �K at ���C and almost equally increase with a temperature�

�

Figure ���� Cross�section of the LE target�

1

Figure ���� The ANSYS model of a target segment�

�

Figure ���� The average power deposited in di�erent elements of the LEtarget design�

�

Figure �� � Time evolution of temperature at the center �top� and tem�perature distribution along the vertical axis �bottom� in a target segmentwith the highest energy deposition density�

�

Figure ���� Time evolution of stresses at two points of the beam axis planein a target segment with the highest energy deposition density�

�

Figure ��� Time evolution of stresses at two points of the beam axis planein a target segment with the highest energy deposition density�

�

ANSYS 5.5.3 MAY 15 200116:05:30 PLOT NO. 1NODAL SOLUTIONSTEP=3 SUB =8 TIME=13.3 SX (AVG) RSYS=0DMX =.104E-04 SMN =-.116E+08 SMNB=-.123E+08 SMX =.204E+08 SMXB=.217E+08

1

MN

MX

X

Y

Z

-.116E+08 -.808E+07 -.453E+07 -967500 .259E+07 .615E+07 .971E+07 .133E+08 .168E+08 .204E+08

ANSYS 5.5.3 MAY 15 200116:06:30 PLOT NO. 1NODAL SOLUTIONSTEP=3 SUB =8 TIME=13.3 SY (AVG) RSYS=0DMX =.104E-04 SMN =-.266E+08 SMNB=-.269E+08 SMX =.270E+08 SMXB=.282E+08

1

MN

MX

X

Y

Z

-.266E+08 -.206E+08 -.147E+08 -.874E+07 -.279E+07 .316E+07 .912E+07 .151E+08 .210E+08 .270E+08

Figure ���� Stress distributions after the beam spill �t � ��s� in a targetsegment with the highest energy deposition density�

�

ANSYS 5.5.3 MAY 15 200116:08:01 PLOT NO. 1NODAL SOLUTIONSTEP=3 SUB =8 TIME=13.3 SZ (AVG) RSYS=0DMX =.104E-04 SMN =-.354E+08 SMNB=-.357E+08 SMX =.986E+07 SMXB=.101E+08

1

MN

MX

X

Y

Z

-.354E+08 -.303E+08 -.253E+08 -.203E+08 -.153E+08 -.102E+08 -.522E+07 -191698 .483E+07 .986E+07

ANSYS 5.5.3 MAY 15 200116:09:05 PLOT NO. 1NODAL SOLUTIONSTEP=3 SUB =8 TIME=13.3 SEQV (AVG) DMX =.104E-04 SMN =203314 SMX =.245E+08 SMXB=.257E+08

1

MN

MX

X

Y

Z

203314 .290E+07 .560E+07 .830E+07 .110E+08 .137E+08 .164E+08 .191E+08 .218E+08 .245E+08

Figure ���� Stress distributions after the beam spill �t � ��s� in a targetsegment with the highest energy deposition density�

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References

��� Advanced Conceptual Design of the LE Target and the Beam Plug�Protvino� ����� NuMI�B�� ��

��� Dynamic Stress Calculations for ME and LE Targets and Results ofPrototyping for the LE Target� Protvino� ����� NuMI�B����

��� N�V� Mokhov� �The MARS Code System User�s Guide�� Fermilab�FN��� ������� N�V� Mokhov et al�� �MARS Code Developments��Fermilab�Conf������� ������� N�V� Mokhov and O�E� Krivosheev��MARS Code Status�� Fermilab�Conf������� ������� http���www�ap�fnal�gov�MARS��

� � Poco Graphite Inc�� A Unocal Company� ��� South State Street� De�catur� Texas ��� �

��� B�S�Wilkins� J� of Materials� ����� ��� ������� B�S�Wilkins andA�K�Reich� AECL� �� �������

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