notes on fea modeling of coilgun mass accelerator bill slade

34

Upload: others

Post on 09-Feb-2022

5 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

����������� � ��� � ������������ ��� ���������� ! "#�$��&%'%'���(��)*"+�,�-)

./102043*06587,9;:=<>?5A@$B=58CEDGFIH,:KJ8H;HAL

M NPORQ SUT�VXWZYQ[T]\ Q+^`_,abdcfe�gihkj'limonqpsrXt�eXuwvxc vzyIh{js|~}]}�r�e�msh{t[�{vx�icit(gir�m���jog�nq�Uc h{cf��hk���imsr-�q��h{j'}]nI��rX�{r��

��hk���imor����`bd�{�k�ijseom�v�eoh{n�c�nx�*johkci���kr[jse�vx��r#nx��vzyIh{js|~}]}�r�e�msh{t[�{vx�icit(gir�mUtXn�hk�2�

�'gir��{vx�icit(g�rXm�t�n�h{�=t�n�cijohkjseoj�nx�'ed��nRn�m�eogimor�r�}�vxh{c�tXn�}]l�n�cirXc�eoj���r�yItX�{���ih{ci�eogir4��mohk�~hkci�#tXh{mstX�ih�e�m�|i����t�n�h{�ijsgir�vze�g�� hk�8limor�jorXc�e(��u�t�n�h{�i�Uhkci�ihkci��j=vxci�]e�gir�}]nq��vx¡��{r¢�£;¤q¥§¦*¥¨¦$©�ªq«2©�¬®­*¯°«2±s©�­1±sª[²�³#´$±o¯�µ�¶s·q¸�¹�º�º�»Eµ?¼I©�¦�­$½�²�ªq¥¿¾z±oªÀ²�³�Á�©�³Âµ`¶sºz¸x¹�º�º�ÃzµÅÄÅÆÇ­1¤q²�ÈqÉ�¤

­1¤q±*©�ÈE­2¤q²�«w¤�©�¦Ê­2«1¥§±sª�­2²=Ë�±s±�Ì�­2¤q±Å½'©�³�Èz¦2¯°«2¥ÇÌq­w±�«2«1²�«�Í{¬Î«1±s±�¸(­2¤q¥¨¦wÏA²�«2ËK½'©�Ð�¯�²�³X­2©�¥Ç³'¦1²�½�±Å±�«2«2²�«6¦�µÑqÈq«1­1¤z±�«2½�²�«1±�¸~­2¤q¥¨¦KÏA²�«2Ë�¤z©�¦=³q²�­�Òx±�±s³Ì�±s±�«�«1±sÓX¥§±�ÏA±sªÂ¸i¦1²�©�³XÐ�Ìq«2²�Ìx²�¦1¥¿­2¥Ç²�³z¦=©�³zª-©�¦2¦�±s«�­2¥Ç²�³z¦¦�¤z²�Èqƨª#Òx±�­2©�Ë�±�³�Ï?¥¿­2¤�©4É�«6©�¥§³�²�¬8¦1©�Æ¿­oÔ�£;¤q¥¨¦,¥¨¦�©4ÏA²�«2Ë�ÍÕ¥§³EÍ{Ìz«1²�É�«2±s¦2¦�¸x¦�²+¯6¤z©�³qÉ�±s¦s¸Â¯°²�«1«2±s¯°­1¥§²�³z¦©�³zª[©�ªqªE¥Ç­1¥§²�³z¦$Ï?¥ÇƧÆ~Òx±=½'©�ªE±`²(Ó�±�«;­2¥Ç½�±�µ?£;¤q±�©�ÈE­2¤q²�«ÅÏA±�ƨ¯°²�½�±s¦Å©�³XÐ+¯°²�½�½�±s³�­6¦�¸�Ö�Èz±s¦�­1¥§²�³z¦$²�«¯°²�«1«2±s¯°­1¥§²�³z¦8²�¬i±�«2«1²�«2¦A©(­ÅÒz¥ÇƧÆkµ ¦1Ƨ©�ªE±�×*¥§±�±s±�µ ²�«2Ézµ

Page 2: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

lÊv�|~�{n�vx�f�1v�mo}�v�e��imsr�n�m*limonzpsr�t�eoh{�{r��$e�nÀ¡�r��{vx�icit(gir��;�,�'gir'}]n~�irX�I�irXjstXmohk¡8r��h{c�eogih{j��n�m���h{j���vx�{hk��� n�m4mor��{�it�e(vxcit�r��Õv��icit(gir�moj� e�gÊv�e+mor��k| n�c e�g�r�}�v���cir�eoh{t�limonxl8r�mse�hkrXjnx�`eogir-vxms}�vze��imsr�� n�m+vxtXt�rX�{r�m�v�eoh{n�cÊ��vxj4��r��{�,v�j[h{ci���it�eoh{n�c �Õvx�ic�t(girXmsj]� �Ugihkt(g morX��|n�cfhkci�i�it�rX��tX�imsmorXc�eoj+n�c�e�g�r�v�mo}�v�e��imsr[� n�mUvxt�tXrX�krXmov�e�hkn�cw���

� � T��]QÀ_�� V��RY Q��� �^`V�T�����'gihkjUlimon�¡��{rX} morXl�morXjsrXc�e�j[vxc hkcÂeorXmsrXjseoh{ci�}]h�yfn��,�{��}�l�rX�ftXhkmot��ihke��Â�Êvxc�eohke�hkrXjU�{h��xrt��imomsrXc�e�v�ci� �xn��ke�vx��rfvxj-��rX�k�Uvxj��ÊrX�k���Â�Êv�cÂeohkeoh{rXj�kh��xr�}�vx��c�r�e�hkt���r�t�eon�m�l�nxeorXc��eohÕvx�1u*}�vx��cir�e�hkj�v�eoh{n�c�vxci� j�e�msrXjoj����#r�eoeoh{ci� moh{�xgÂe�h{c�e�n hkeXu�e�gir���nE��r�mocihkci� js|~jseorX}r��~�iv�e�hkn�cij�vxmorÀ�xhk��r�c�� nxmUvxc��! #"$�d�kh���rÀtXh{mstX�ih�e���jsginE�Uc hkc �*h{���imsr&%���h{c��°�q�'���)(����

Launcher

RC

current I

V

Vc

l

coil

Loop

(including coilseries resistance)

Moveable core

��h{�x�imor&%I�$*~t(girX}�v�e�hkt#nx�*eogir#johk}�li�kr+�, -" tXnxh{�{�x�ic��Õvx��cit(girXm��.0/2143576�8:9<;>=:? 1A@CB@ED 8GF / 3 ; H I<JKMLONEP ���q�

.Q/ B H 3 �R%��3S 3 SUT 6 e(v�cig 1 � 5WV 8 �E� S 3 S5WV�5W6 T 6 ; H 9 �)X��

8>Y Z @CB@ED\[^]`_ H a!b J =dc �fe�%

Page 3: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

�c H 8 J� ������576 ��� ��V 8�� S 3 S � � V � �

� ��� V ��� 8�� S 3 S ����� H � �����

Y����� � [��-]�� H � �� ��!#" �F�8$�&% 3(' H ) ��*��

�+ 8-, H ) �)(���'gir�jo�il�rXmsl8nxjorX� �inxeoj4v�¡8nE��r c vxci� F mor�limor�jor�cÂe+v-�irXmshk��v�eohk��rÀhkc�e�h{}]rx��'gir mor��Õv�eoh{n�cijsgih{l �°�q��h{j�ps�ij�e/. vzy~��r��{��0¿jf}�v���cir�eoh{t��Êr��{� tX�ims�#r �Â�Êv�eoh{n�c h{c

�ihkjo����h{jor�����r�}�r�}�¡�rXmohkci��e�giv�e1 H 3576 8:9 �°� ) �

vxc��feogÊv�eUe�g�r�t��imomsrXc�e4h{cit��{�i�ir�jUvxc�h{}]l8n�jsrX��t�n�}�l�n�cir�c�e

2 H I JKUL NEP �°���q�vxj'��rX�k�?vxj�vxc�h{ci�i��tXrX��lÊvxm�e��

2436587 H ? 1 8 @CB@ED =�F / 3 ;:9 �°�^%���Ugir�mor F / 3 morXl�morXjsrXc�e�j�e�gir4h{ci�i��t�e�hkn�c]r<;8rXt�eoj��Uhkeogih{c]}]nq�~hkci��livxmseojÀ� eogir4vxmo}�vM�eo�imor��Uv�j'jorXr�c hkcfeogir#�Õvx¡�n�mov�e�n�m�| � mor�jse���� movx}�r �dnx� �6mor�� rXmor�citXr���'gir[jsrXt�n�ci�fr �Â�Êv�eoh{n�c �R%��`h{j?ps�ijse�e�gir[��r��Êcih�e�hkn�c�nx�?eogir+msrX�{v�e�hkn�cijog�h{l�¡�r�ed��rXr�c

}�vx��cir�e�hkt]�xrXt�eon�m�l�nxe�r�c�e�hÕv���v�ci� e�g�r�}�v���cir�eoh{t>=Ê�Iy �irXc�johked|x� �'gir�msrX�{v�e�hkn�cijog�h{l¡�r�ed��rXr�c }�v�e�r�moh{vx�=}�vx�xcir�eoh{j�vze�h{nxc 9 vxci� e�g�r�}�v���cir�eoh{t?=Ê�Iy ��rXcijshked| hkj���h���r�chkc �fX����A@4n�e�rÀe�gÊvze�eogih{jUhkjUv]jsh{}]li�{h �ÊrX��}]nI��rX�?nx�$� rXmsmon�}�vx��cir�e�hkjo} eogÊv�e��in~rXj�cinxehkcitX�k�i�irÀg�|~jse�r�mor�joh{jB®�DC2�E �Â�Êv�e�hkn�c �feÂ�+hkj&FÀh{mot(g�ginx�<0Çj[�xn��ke�vx��r-�Õv�� nx�Ke�gir �, #" tXhkmot��ihkeXu;nx�K�Ugih{t(g�e�gir�{vx�icit(gir�mUtXn�hk�A� n�mo}]jUvlÊvxmseX�=�'gir#h{c�e�r���m�vx�An�c�eogir#�{r�� e �dgivxci���6joh{��rÀmorXl�morXjsrXc�e�j�e�gir

X

Page 4: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

�xn��ke�vx��r[v�tXmonxjoj�e�g�r[tXn�hk�8�Uhkci�ih{c���jX�,b6e�h{j�v��kh{cir4h{c�e�r���m�v���e�v �xr�c�nE�xrXm�e�g�rÀ�{rXc��xe�g�n��eogir��Uhkci�ihkci��jUe�gÊv�e4rXc�tXh{mstX�kr�eogir�t�n�h{�1���'gihkj4hkj4�ih��]tX�i��e�eon�r��xv��{�Êv�eor���h{mor�t�eo�k|fvxc��msr �Â�ih{msrXjÀe�g�r-�ijor]nx��v���e�msh{t ����e�nfjohk}�li�khk� |�hke+� n�mÀcÂ�i}�r�mohkt�vx�,��jor � �Ugihkt(g �Uh{�{�*¡8r�ir�jot�h{¡�rX��h{c *IrXt��$X�� %~� *�����'gir�c�r�y~e[r��~�iv�e�hkn�c msrX�Õvze�rXj�h{c�jse(v�cÂe�vxcir�n��ij[t(gÊv�ci��r�hkc eogir�tXvxlÊvxt�hke�nxmU�xn��ke�vx��r

eon�e�g�r�t�n�h{�?t��imomsrXc�e����'gih{j�h{j�tXnxcÂ�xrXcihkrXc�e[¡�rXtXvx�ijsr�e�gir�h{c�hke�h{vx�;t�n�ci�ih�e�h{nxcijUn�c eogih{jr��~�iv�e�hkn�c�vx�{�knq� eogir#�ijor�m�eon]jsr�eUe�g�r��imoh{c��]r�cirXms�x|�nx�*e�gir#j�|Ij�e�r�} �bdc n�ms�irXm+eon�tXnx}�li�Ie�r�eogir�� n�mstXr�nxc e�gir�limonzpsr�t�eoh{�{r�uAh�e+hkj+cir�tXrXjsj�vxm�|Re�n��ir��Êc�r

ginE� e�g�r �ÊrX�k� r�yIt(gÊv�ci��rXj�}]n�}]rXc�e���} �Uh�e�gZeogirRlimsnzpsrXt�e�hk�{rx���Ên�mseo�icÊv�eorX�k|xu�e�girr��{rXt�e�msn�}�v���cir�eoh{t �Êr��{� r �Â�Êv�eoh{n�c�j�vx�k�{nE� �ij#e�n�tXn�cij�e�ms�it�e�e�gir �ÊrX�k��j�e�msrXjoj�e�r�cijon�mjsginE�Uc n�c � ��������| h{c�e�r���m�v�eoh{ci��e�gihkj-nE��rXmvRjs�ims��v�tXrfjo�imsmon���ci�ih{c��Re�gir�r�yIeorXmsh{n�mnx�$e�g�r�v�mo}�v�e��imsrxui��joh{c�� �� ���uieogir#�{n�c���hkeo�i�ih{civx��� nxmotXr#n�c�eogir�l�monzpsr�t�e�hk�{rÀhkj'mor�v��ih{��|t�n�}�l���e�r�� vxj�v�� �icit�eoh{n�c nx��e�g�r �ÊrX�k� jseomor�ci�xe�g v�j���rX�{��vxj�eogir�l�n�jshke�hkn�c n���e�girvxms}�vze��imsrx� �'gir vxtXt�rX�krXm�vze�h{nxc nx�#e�gir�v�mo}�v�e��imsrRh{j�h{c�e�r���m�v�eorX� hkc ��*���v�ci� e�girmsrXjo���ke(v�cÂe'�xrX�knIt�hked|�hkj'�ijor�� e�n��Êc���eogir�vxmo}�v�e���morÀl�n�joh�e�h{nxc�h{c �)(�����Ên�mK}�n�msr4t��Õvxmsh��ÊtXv�e�hkn�cn�c�eogir4��vxmshÕvx¡i�krUcÊvx}]rXj���jorX��hkc�eogir+r��~�iv�e�hkn�cijXuI��v�¡i�{re]� n��ici�Rhkc�4lil�rXci�ihÎy b'h{c *IrXt��!e��xhk��r�j4eogir���r��Êcih�e�hkn�cij�nx�,e�g�r�mor��Õv���r�c�eÀjs|~jseorX}

j�e(v�eor#��vxmshÕvx¡��{rXj�vxj'��r��{�Åvxj�eogir#mor �Â�ihkmor�� }�v�e�r�moh{vx�At�nIr��t�h{r�cÂeojX�� ��T]W���V��RY ^`ORQ �*a��*^�QÀ\ Q+��� �^,VXT ��� ���� ��������������� ��!"�#�$ gihk�{rRh�efh{j�eogirXn�msr�eoh{t�v��{�k| l�n�jojsh{¡i�krRe�n jon�����r e�gir�t�n�}�l��{r�eorX��| �icih �ÊrX� lig�|~johkt�vx�limsn�¡i�krX} hkc�vÀ}�vxcicir�m=joh{}]h{�{vxm*eon(BÎ�DC1uÂhke=hkj`}�n�msrUtXn�c���r�cih{r�c�e�eon�jsli�{h�e,e�gir�limsn�¡i�{r�}hkcÂeon�hkeoj[e�gimsrXrtXn�}]l�n�cirXc�e#js�i¡ijs|~j�e�rX}]jX�#e�g�r-�Õvx�ic�t(girXm#}�vx��cir�e�h{t �ÊrX�k� l�mon�¡i�krX}�ueogirtXh{mstX�ih�eÀlimsn�¡i�{r�} vxc�� eogir]vxmo}�v�e���mor �Âh{c�rX}�v�e�hktXjX���'gih{j#}��ij�e#¡8r�inxcir-�Uhke�gjsn�}�rftXvxmor�u�johkcitXr vx�k��e�gir�jor�jo�i¡�js|~jseorX}]j�vxci� e�gir�h{m-j�e(v�eor���vxmshÕvx¡i�krXjvxmsrftX�{nxjorX��|t�n��ili�krX�;����vx¡��{r�����h���r�j�eogirXjsr�jse�v�e�r��vxmoh{vx¡i�krXj#vxci� e�gir]limsn�l8nxjorX��}�r�e�gin~�ijÀ� n�mjsn��k�~h{c���� n�m�e�gir�} �

��&% ')(�*,+-�.!/��* 01*32"*345*3�6�879�#2��:��!"�#�<;=�#�8>#*?� ���@�BAC�D��*3����!FEG2��|�vxjsjo�i}]h{c���e�gÊvze�e�g�r4e�g�morXr �d�ihk}�r�cijohkn�cÊvx�wt�n�h{��h{j�vzyIh{j�|I}]}]r�e�msh{t�u~eogir+limsn�¡i�krX}Ph{j��msr�v�eo�k|-jsh{}]li�{h �ÊrX�¡�rXtXvx�ijor���r4t�vxc�cinE� e�msr�v�eKe�g�r4limsn�¡i�krX}Pvxj=ed��nM�d�ihk}�r�cijohkn�cÊvx�1uvxjUjsrXrXc�h{c���hk���imsr�X��

e

Page 5: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

��vx¡��{r-���=�*vx¡i�{rÀn���j�|Ij�e�r�} j�e(v�eorÀ�xv�mohÕv�¡i�{r�j� N���� N�� _ � ����� � ��������� � � � _ F ����� � � � �������B . v���cir�eoh{t[�xrXt�eon�m�l8nxeorXc�e�h{vx� ��h{c�hke�r#r��{rX}]rXc�eÀ}]r�eogin~� �Uhkeog� �i�{��|�hk}�l��{h{t�hke=e�hk}�rÀj�e�r�lilih{c��i�b "�n�h{�;t��imomsrXc�e "�m�vxc � � @4hktXn��kjon�c�e�hk}�r+jse�r�lilihkci�� ��hkmohkci��t�v�lÊvxtXh�e�n�m��xn��ke�vx��r "�m�vxc � � @4hktXn��kjon�c�e�hk}�r+jse�r�lilihkci�� �+ms}�vze��imsr[��rX�knIt�hked|

"�m�vxc � � @4hktXn��kjon�c eoh{}]r hkc�e�r ���m�vze�h{nxc ��joh{c�� r�yIeom�vxl�n��{v�e�r��� n�mot�r limsrX�ihkt�eoh{n�c limonE�~h{�ir��� mon�} �ÊrX�k�fjon��k��e�hkn�c;�� �4mo}�v�e��imsr#l8n�jshkeoh{n�c "�m�vxc � � @4hktXn��kjon�c�e�hk}�r+jse�r�lilihkci�

��hk���imsr!XI��bd�{�k�ijseom�v�eoh{n�cnx�;joh{c����{rUjse�vx��r�nx�ÅvzyIhkjs|~}�}]r�eomohkt'�Õvx�ic�t(girXm�tXn�hk�ie�morXv�e�r���vxjv�ed��n �d�ihk}�r�cijohkn�cÊvx�8��rXnx}�r�e�ms|x�

� citXr4��r4gÊv���rÀrXj�e(vx¡��{h{jsgirX�]e�gir+�irXjsh{mor���tXnxh{�w��rXnx}�r�e�ms|xu~��r[tXvxc��ihkjotXmsr�eoh{jor�e�girt�n�h{�=h{c�eonRjo}�vx�{�`eomohÕv�ci���i�{vxm� �Êcih�e�r�r��{r�}�r�cÂeojXu ��nq�xrXm��Ugihkt(g e�gir �ÊrX�k� h{j�vxlilimsn�y �hk}�v�eorX���ijsh{ci� v jor�e�n��'�ijor�m �6�ir��Êc�rX� ¡Êvxjsh{j#� �icit�e�h{nxcij B % C1u B X CK�{h��xr-e�g�n�jor�jorXr�c h{c��hk���imsrei����! ��#" $ � � � N%�&� � � N%�&� � N _ ' �(� � F _ N%����� �. v�cÂ|�mor�jorXvxmot(gir�moj B e C � B � C�vxlilimsn�vxt(g�eogir �Êcih�e�rKrX�krX}]rXc�e,jsn��{��eoh{n�c�nx�Ê}�vx��c�r�e�hkt$�irX�{�r��~�iv�e�hkn�cijU�ijohkci�-e�gir#t�n�citXr�l�e4nx��msrX�k�it�e�vxcitXr�uÊh2�¿rx�.0/*)E.Q/ B H 2 9 �°� X��

Page 6: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

��hk���imsr ei� E�y�vx}]li�{r �Êcih�e�rUrX�krX}]rXc�eK}�r�jog�nx�;�{vx�icit(gir�m�t�n�h{�1� @�nxe�r'eogir4hkc�e�rX�xm�v�eoh{n�clÊvze�gZ� �Ugih�e�r]morXt�e(vxc����{rrXc�tX�{nxjoh{c���eogir�v�mo}�v�e��imsrE�4� n�m#t�n�}�l���e�hkci��eogir]vxmo}�v�eo�imor� n�mstXr��

�Ugir�mor ) h{j�e�g�r�msrX�k�it�e�vxcitXr���vxcÊvx�kn���n��ij�e�n�mor�joh{j�e(vxc�tXrxu�n�m-mor�joh�e�hk�~h�ed| h{c r��{r�t�e�msh{tt�h{mot��ihkeoj[vxc�� js|~jseorX}]j(���#�'gir�morX�k�it�e�vxcit�r-t�vxc ¡�r�t�n�citXr�l�e��ivx�{��| �ir�jot�moh{¡�rX��v�j+e�girrXvxjor��Uhkeog �Ugih{t(g e�g�r�}�vx��c�r�e�hkt �Êr��{� �{hkcirXj-tXvxc l8r�cir�eom�v�eor�e�girf}�v�e�r�mohÕv��2��b6eh{j��r�cirXmovx�{��|�vcin�c �d�{hkcir�v�m �Â�Êvxc�e�h�ed|�e�gÊvzeUtXn�}]li�{hkt�v�eorXj�eogir#jon��k��e�hkn�c�nx����� X����

$�r limon�l�n�jsr�vxc vx�keorXmociv�e�h���r vxl�limon�v�t(g �Ug�rXmor�u+hkcijseor�vx� nx��mor��{�it�e(vxc�tXrxu�e�gir}�vx��cir�e�hkj�v�eoh{n�c���n�m;}�vx��c�r�e�hkt,l�n��Õvxmsh{jov�e�hkn�c4��rXcijshked|��;h{j;�ijsrX�#e�nUr�yIli�{vxh{c[eogir`lig�|~johktXjnx�$e�g�r�v�mo}�v�e��imsr#vxci�ftXnxh{�;jsgir�v�eog;�*~e�vxmseoh{ci��� msn�} . vzy~��rX�k��0¿j�}�vx��c�r�e�hkt �Êr��{�fr �Â�Êv�eoh{n�c

.0//1 H 2 = @ �@ED 9 �°��eÂ�vxci� jo�i¡�jse�h�e���eoh{ci�R��� ) �'hkc�e�n ����eÂ�'vxj���r��{�$vxj�h{��c�n�mohkci�-e�gir#e�hk}�r#�ir�mohk��v�eohk�xr�n��� ��¡�rXt�v��ijor-e�g�h{j+eorXmo} h{j+�xrXms|�js}�v��{�*v�eÀe�gir�eoh{}]r�jotXvx�{r�j[��rt�n�cijohk�irXmÀg�rXmor�uÅh2�¿rx�

eogirÀ� mor �Â�ir�cit�|fhkj'��rXm�|f�{nE�4��uI��r#��r�e.Q/ 1 3576 8:9 ; H 2

�°�����*IhkcitXrÀe�g�r�}�vx��c�r�e�hkt =Ê�Iy���rXcijshked|�hkj'�ir��Êc�rX�Rv�j3 H .Q/ B �°� ���

hkc]eorXmo}]jKnx�Aeogir4�xrXt�eon�m�l�nxeorXc�e�h{vx� B u�e�gir��ÊrX�k��r��~�iv�e�hkn�c]eogÊv�eK��r��Uh{jsg�e�n�jon�����r�h{j.0/ 1 �576 .0/ B 8G9 ; H 2�

�°�� ���

Page 7: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

bdce�gir�limor�tXr��ih{ci��r �Â�Êvze�h{nxc;uÂhke`hkjKhk}�l�n�m�e(vxc�e,eon�msr�vx�kh{jsr�e�gÊv�e=eogirUtX�imsmorXc�eKe�r�mo}2 h{j�morXvx�{��| vftXn�}�¡ih{cÊvze�h{nxc n���jor���r�m�vx�Ke�rXms}�j�vxci��e�g�r�}�vx��cir�e�h{jov�e�hkn�c 9 ��vxmohkrXj�ir�l8r�ci�ihkci�-n�c�eogir[}�v�e�r�mohÕv�����ci�irXm't�n�cijsh{�ir�m�v�eoh{n�c;� �+j�hk�{�{��jse�mov�e�r���hkc���hk���imor �Iuivt�n�cijor��Â�irXcit�r�nx�Åeogih{j'hkj�e�gÊv�eUhkc�r�vxt(g vxmsr�v�uÊv-�ih ;Ar�mor�cÂe���� E cirXr��ij�eon¡8rÀjsn��k�xrX�;�

��hk���imor �~�$�#nE��r�mocihkci���ÊrX�k� r��Â�Êv�e�hkn�cij'hkcfeogirÀ��vxmohkn��ij � nxcirXj����hkmojseXu~eogirXmsr[h{jKe�gir+�imoh��Ihkci��t�n�h{��tX��momor�c�e 2 b �Ugihkt(g�r�yItXh�e�r�j�e�gir[}�vx��c�r�e�hkt,�irX�{�hkcZe�gir js|~jseorX}�� �'g�rXmor�v�morRv��{jon h{ci�i��tXrX� t��imomsrXc�e�j�hkcZe�gir jogirXv�e�g vxci� vxmo}�vM�

eo�imor�uA�Ugih{t(g eorXci�Reon�r�yIl8r���e�g�r�}�v���cir�eoh{t��{h{c�rXj+n��K� nxmotXr���¡�| eogir �sj �~hkc��dr ;Ar�t�e �Â��ueogirXmsrX¡�|ft�vx��joh{c��]�kn�jojsrXjUvxc�� msrX�i�it�e�hkn�cfh{cfvxt�tXrX�krXmov�e�hkn�c;�,�'gir�jor�tX�imsmor�cÂeoj4hkcitX�k�i�ir

Page 8: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

eogir#jogirXv�e�g�tX�imsmor�cÂeoj 2 jsgir�vze�g H 8,? jogirXv�e�g @CB@ED �°� *��vxj���rX�k��v�j�eogir�tX�imsmorXc�eoj h{c��i�itXr���n�c e�gir vxms}�vze��imsr�v�j v mor�jo�i��e n���t(gÊvxc���h{ci�}�vx��cir�e�hkt �ÊrX�k��vxci�fe�gir�vxms}�v�eo�imorÀ}]nxeoh{n�c;u~�~h � �

2 vxmo} H 8,? vxmo} 1 @CB@ D 8:F v�mo} / 3 ; �

�°� (��$ hkeog]vx�{��eogih{j`hkc}�hkci�;u���r4gÊv��xr�eogirUtXn�}]li�{r�e�r4�Êr��{�]r �Â�Êv�eoh{n�chkceorXms}�j=nx��e�gir

t�n�h{�;��mohk�~hkci�-tX�imsmor�cÂeX�

.Q/ 1 �576 .0/ B 8G9 ; =:? 1 @CB@ D 8:F />.0/ B ; H 2 b �

�)% ) ��'gir}�v�e�r�mohÕv��*t�n�ci�i�it�e�h��Ih�ed| ? h{j+jor�eÀeon�e�gir-t�n�ci�i�it�e�h��Ih�ed|Rnx�=eogir-jogirXv�e�g�� n�mr��{rX}]rXc�eoj-h{cijsh{�ir�nx��e�g�r�jsgir�vze�g vxci� e�n�e�gir�t�n�ci�i��t�e�h��~hked| nx��e�g�r v�mo}�v�e��imsr�� n�m

eomohÕv�ci���{r�j��Uhkeogih{c eogirfvxms}�v�eo�imor�� �'girf��r��{n~tXh�ed| F nx��e�gir�jsgir�vze�g h{jvx����v�|~j]vxj �js�i}�r�� � rXmsn��Ugihk�{r�eogir-��rX�knIt�hked| nx��eogir�vxmo}�v�e���mor��ir�l8r�ci�ij�n�c e�girr��xn��{�Ie�h{nxc n��eogir�vxmo}�v�e���morÀ}]nxe�hkn�c�vxj'e�hk}�r+lÊvxjojsrXj���'gir�}�vx��c�r�e�hkj�v�eoh{n�c���nxm�}�vx��cir�e�h{tKl�n��Õvxmsh{jov�e�hkn�c 9 �?�Uhke�g�h{c�eogir�jsgih{r��{�-vxc�����n�mvxms}�vze��imsr�h{j#�ir�e�rXms}�hkcirX� � msn�} v�johk}�l��{r-vx�k��rX¡�m�vxhkt�mor��Õv�eoh{n�cijsgih{l�vze#r���r�ms|�l�n�h{c�e

� n�m+� n�m�e�gir� E .��;v�eÀr��xrXm�| cin~�ir-l8nxh{c�e����&@4nxeor�e�gÊv�e[h{c n��im[vzyIh{js|~}]}�r�e�msh{t�� nxm �}����Õv�eoh{n�c;u~e�gir�}�vx��cir�e�h{jov�e�hkn�c�h{j�v-��r�t�e�nxm��Uh�e�g v]movx�ihÕv����vxci� v]�kn�ci��h�e��i�ihkcÊvx� +t�n�}�l�n�cir�c�eUh{c�e�r�mo}]j�n�� 3 v�j

T V H T 6 � VS 3 S e(vxc�g 1 � 5WV 8 �q� S 3 S5 V 576 T 6 ; �)%I�q�T � H T 6 � �S 3 S e(vxc�g 1 � 5WV 8 �q� S 3 S5 V 576 T 6 ; 9 �)% %��

�Ugir�mor S 3 S H � � �V = � ���

�)% X��T 6 h{j+eogir-}�vzyIh{}��i} vx�k�{nE��r�� }�v���cir�eoh{jov�e�hkn�c nx�=eogirvxmo}�v�eo�imor���jogirXv�e�g�}�vM�eorXmoh{vx�=vxci� � 5WV � hkjÀe�gir]�{nE�4� �irX�{� }�vx��cir�e�h{t-msrX�{v�e�h���rl8r�mo}]r�vx¡�h{�{h�ed|���'gihkj�}]nI��rX�r�y�g�h{¡ih�e�j�eogir+t��Õvxjsjohkt � *`�6tX�im���r �-j�v�eo�im�v�eoh{n�c�¡8r�gÊv��~h{n��im�uI¡���e'hke�jog�n��i�{��¡8r4morX}]rX}��¡�rXmsrX��e�gÊv�e#h�e#h{j#vxc vxl�limon�yIh{}�v�e�hkn�c nx�Ke�gir-eomo�ir�� r�momonx}�vx�xcir�eoh{t�¡�rXgÊv��~h{nx�imX�?@4ng�|~jseorXmor�johkjXu�vxcihkjonxeomon�l�|�nxm�nxe�g�rXm'tXnx}�li�kh{tXv�e�r���� rXmsmon�}�vx��cir�e�hkt[¡8r�gÊv��~h{n��imsjUvxmorÀhkc��t��{�i�ir��;��4nE��r��xrXmXu4e�gihkj�}]nI�ir��+v��{�{nE�Uj]e�girRl�n�jsjoh{¡��{rRhkcitXn�msl8nxm�v�eoh{n�c nx�À��vxmohkn��ijjsrX}]h �dr�}�l�h{mohkt�vx�w}�vx��cir�e�hktÀ}�n~�irX�kjXuIhk�$�irXjsh{msrX�;�

*

Page 9: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

���! �� ��� � � _ �-N ��� � � ����'gir�h{}]limor�jojsrX� t�n�h{�=t��imomsrXc�e 2 t�vxc�¡8r�vxlilimsn�y�hk}�vze�rX� h{c�e�r�mo}]j�n���e�gir]tX��momor�c�e=ÊnE�Uhkci��eogimonx�i��g�eogirU�Uh{ci�ihkci��j�uÂeogir�c~��}�¡8r�m�n��Ae���mocij I v�ci��eogir4t�mon�jsj �6jorXt�e�hkn�cÊvx�vxmsr�v-nx�$e�gir#t�n�h{� ��� K � ����� H � b H K [ L v�j2 b H I<JK L NEP 9 �)% eÂ��Ugir�mor N P morXl�morXjsrXc�e�j�eogir[v � h{}���e�gÊv��Ê�icihkeK��r�t�eon�mXu K hkjKeogir4�Uhkci�ihkci���krXci��e�g�v�ci� Lhkj�e�girÀ�Uh{c��ih{ci��eogih{t �Âcir�joj���Àhk��r�c�e�girÀ�Uh{msrÀ��vx�i�xr��jsrXr-�+lil�rXci��h�y�bsbK� nxm'�ihÕvx}]r�eorXmsj�¡ÊvxjsrX��n�c�4}�r�mohkt�vxc�Uhkmor���vx�i��r�u~eogir+}]r�eomohkt��Uhkmor��ihÕvx}]r�eorXmsjK� n���ci��hkc E`�imonxl8r+vxci��r��{jor��UgirXmsr[jog�n��i�{�¡�r jsrX��� �dr�yIli�{vxcih�e�n�m�|i��u��krXci�xeog vxc��Z�Uh{��eogZnx�+e�gir tXn�hk�2u�h�e]h{j]jse�movxh{�xgÂes� n�ms��vxms� e�nt�n�}�l���e�r#e�gir�}�vzyIh{}��i} cÂ�i}�¡�rXm�nx��eo�imocij+vxci� �Õv�|�r�mojUe�gÊv�e4t�v�c �ie�h{cfe�g�r���h���r�cjslÊvxtXr�� "�n�cijohk�irXm'eogir#��rXn�}]r�eoms|��xhk��r�c hkcf��h{�x�imor&���

�*h{���imsr&���`bd�{�k�ijseom�v�eoh{n�c�nx�*eogir#mor��Õv���r�cÂe4�ihk}�r�cijohkn�cij�� n�m�eogir#tXn�hk� �6lÊvxt �Âh{ci����Êmon�} e�gihkjXu`��r�tXvxc �irX�i��tXrfe�gÊv�e-eogir�cÂ�i}�¡�rXmnx�Ue���mocijl�rXm�Õv�|�r�m-tXn�}]r�e�n

vxl�limon�yIh{}�v�e�r��k|

I Z�� h{c�e 1 K] ; 9 �)% ���(

Page 10: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

�Ugir�mor�h{c�eq�1��h{ci��h{t�vze�rXjUv�eomo�icitXv�e�hkn�cfnx�$e�girÀ� m�v�t�e�hkn�c�|~h{r��{�ihkci��e�gir#hkcÂeorX��r�m'lÊvxm�e���'gir�eonxe(v��*cÂ�i}�¡�rXm+nx�=�Õv�|�r�moj+eogÊv�e!�ie[hkc e�gir�e�gihkt �~c�rXjojÀmsrX��hkn�c tXvxc ¡�r�� n��ic��

eon]¡�r�vxlilimsn�y�hk}�vze�rX��|

I � � h{c�e 1 % L� X ] ; �

�)% ����+j=v[t�n�cijsr �Â�irXc�tXr+n���eogih{j�uxe�g�r�e�nxe�vx��cÂ�i}�¡�rXm�nx����l�rXms� r�t�eo�k|���n��ic��w�*e��imscij`t�v�c

¡�r�vxlilimsnEyIhk}�v�eorX��� n�mUv��h���rXcf��r�n�}]r�e�m�|fvxj

I H I Z I � � hkcÂe 1 K] ; h{c�e 1% L� X ] ; �

�)% ��@4n�e�r'e�gÊvzeKeogih{j=}]nI��rX�i¡�rX��hkcij`e�n��{n�jsrUhke�j,��vx�kh{�ih�ed|��Ug�rXc�eogirUtXn�ci���it�eon�m���hÕvx}��

r�e�rXm=¡�rXt�n�}�r�j�vÀjs�i¡ijse�vxc�e�h{vx�i� m�vxt�e�hkn�cnx�8eogir�j��Âh{c]�irXlIe�g �1vxlil�mon�yIh{}�v�e�r���hkceorXms}�jnx�$e�g�r��imoh{c��eoh{}]r[jotXvx�{r�j�vxj

��� ��� � D? b 576 9 �)% *���Ugir�mor � D hkj�eogir�eoh{}]r�jst�vx�kr�n��,e�gir&�Êmohkci�]r���r�c�e�u;h1�Çr���e�gir�joh{}��i�Õv�eoh{n�c�eoh{}]r�j�e�r�lw����Ê�im�e�gir�mo}]n�mor�u=�Ug�rXc e�gir��Uh{c��ih{ci�xjvxmor�eogih{t � �Uhke�g msrXjol�rXt�e�eonRe�girfnE��r�m�vx�k��tXnxh{��ihk}�r�cijohkn�cij�u,e�girfvxjsjo�i}]l�eoh{n�c nx�4vR�ic�hk� n�ms}���|��ih{j�e�mohk¡i��eorX� tX�imsmor�cÂe��rXcijshked| ¡�r �t�n�}�r�j�{rXjsjli�Õvx��joh{¡��{rx� bdc e�gir�h{c�eorXmor�jse]nx�+joh{}]li�kh{tXh�ed|�u`ginE��r��xrXmXu���r�jogÊvx�k�'jseoh{t �eonfeogih{jÀc�nxe�hkn�c nx��vf��h{jseomohk¡i��e�r���tXn�hk�,tX�imsmor�cÂe�vxc����kr�v���r]vxc�h{c��xrXjseoh{��vze�h{nxc nx��h�e�j��vx�kh{�ih�ed|]� nxm�e�girÀ� ��eo�imor��

���! �� � $ � � � � � � � � ��� N%����� � � ' ��� � � N � � � ��� ��� � � �&�(� � � � � � ��� N _ � � ���� _ � � ���� � ��� � � ��� � � � � � � ��|�vxjojs�i}�hkci�v-jo}�vx�{�1uI¡���e��Êcihkeor[e�hk}�r[hkcitXmsrX}]rXc�e�� D ui��r#tXvxc v�lilimon�yIh{}�v�eor+e�gireoh{}]r[�irXmshk��v�eohk��rÀhkc��R% ) ���Uh�e�g @CB@ED � B������ �� 8 B���� �� D 9 �)% (��

�Ugir�mor+eogir[js�il8r�mojstXmohkl�e�j'hkc�lÊvxmsrXc�e�g�rXjohkj�h{c��ih{tXv�e�r�e�gir+�xrXt�e�n�m�l�nxeorXc�e�h{vx�8r���vx�{�Êvze�rX�v�e'eogir�� = � �"!�vxci���#��$�e�h{}]rXj�e�r�lijXuÊmsrXjol�rXt�e�h���rX��|��=bdcfe�gihkj�tXvxjor�u$�R% ) ��¡8r�tXn�}]rXj.0/ 1 �576 .0/ B ����� �� 8G9 ����� �� ; =

? 1 B ���%� �� 8 B ��� �� D 8:F ���%� �� / 3 ����� �� ; H 2 ���%� ��b �

�fX ) �� )

Page 11: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

bdc e�gir �ÊcÊvx��eorXms} uA��r-gÊv���rjs�i¡ijseohkeo��e�r�� 3 � n�m. / B �#�'gih{jÀhkj[¡8r�t�vx��jor-h{ceogir��kh{cirXvxmohkj�v�eoh{n�c�nx��e�gihkj4r��~�iv�e�hkn�c;uÊ��r��Uh{�{�;eomorXv�e4eogih{jUe�r�mo}�uÊe�gir�lÊvxjse4��vx�{�ir�j4n��B vxci� eogir�tXnxcÂ�xrXt�e�hk�xr�eorXms} vxj ��jon��imstXr�j �i���'girfmor�v�jon�c � n�m�e�gihkj��Uh{�{�K¡�rXtXnx}�rt��{r�v�m'h{c�e�gir#t�n�}�hkci�-jor�t�eoh{n�cij��

���! ���� $ � � ��� � N � � ' �(� � F _ N%����� � ' �(� � � � �&�(� � � � � � ��� N _�'gir �Êcih�e�rrX�krX}]rXc�e�}�r�e�gin~� morX�kh{r�jÀn�c�eogir}�hkcih{}]h{jov�e�hkn�c nx��v�msrXjsh{�i�Êv��,� n�mo} n���fX ) �+v�e#rXvxt(g�cir�� e�hk}�r�j�e�r�l � = �js�it(g eogÊv�eÀeogir �Êmoj�e#�xv�mohÕvze�h{nxc � a ��vxcihkjogir�jXu�~h � �

� a<H Y�

.0/ � B ���%� �� [ 1 �576 .0/ B ����� �� 8:9 ����� �� ; ] � =? Y�

� B ���%� �� [ 1 B ����� �� 8 B ��� �� D 8 F ����� �� / 3 ����� �� 8 2 ����� ��b ; ] � �

�fX��q��'gihkj�r�yIlimsrXjojsh{n�cf}]h{cihk}�hkjor�j,e�gir[msrXjsh{�i�Êv�� a uI�Uh�e�g�msrXjsl8r�t�e'e�n�e�gir[c�r�� ��rXt�e�n�ml�nxe�r�c�e�hÕv�� B������ �� js�i¡~psrXt�e�e�n eogir c�rXtXr�jojovxms|Z¡8n���ci�Êvxm�| t�n�ci�ih�e�hkn�cijX� �'gir �irX�{��Â�Êvxc�eohke�hkrXj 3 ����� �� u 9 ����� �� uA2 ���%� ��b u B���� � vxci� F ����� �� / 3 ���%� �� vxmsrfeomorXv�e�r��Zvxj�sjsn��imstXrXj�u � h1�Çr�� e�gir�| vxmsr��xhk��r�c vxj�� �ÂcinE�Uc�� �Â�Êv�cÂeohkeoh{rXj-�Uh�e�gihkc e�girf�{hkcir�v�moh{jsrX�

cinxc��d�kh{cirXvxm�j�|Ij�e�r�} ����! ���� � � � � � � � _ � � � � � �-N � ' F � � �&��� � �4�{� �irX�{��� ��cit�eoh{n�cijUv�mor[msrXlimsrXjor�c�e�rX� h{c�eorXmo}]j'nx�*v-jor�eUnx�#�~c�nq�Uc�¡Êvxjsh{j�� �ic�t�e�hkn�cijnE��r�m�eomohÕv�ci���i�{vxm��Êcihkeor r��{r�}�r�cÂeojX� �Ên�m]�{h{c�r�vxm]vxlil�mon�yIh{}�v�e�hkn�c;uKhke�h{j]rXcin�����gZe�njsl8r�tXhk� |-eogir!�irX�{��n�c�eogimor�r+l�n�h{c�eoj[� cinI��rXj(��uI��jo�Êvx�k�k|li�{vxtXr���v�e=eogir4�xrXmseoh{t�rXj�n��;e�gireomohÕv�ci���{r�jX� �4hk��gir�m�n�mo��rXmoj-msr �Â�ihkmor�jonx�{��eoh{n�c vze-limonx��mor�jojoh���r��k| }]n�msr�l8nxh{c�e�j�� jorXr��hk���imsr& ����

$�mohkeoh{ci��nx��e�eogir]vxlilimsn�y�hk}�vze�h{nxcR� �icit�eoh{n�c�j�hkjÀr�vxj�| vz� e�rXm#t�n�c���rXmsjohkn�c hkcÂeon v�knItXvx���ov�mor�v1�]t�nInxmo�ihkcÊv�e�rÀj�|~jse�r�} �=�'gir#e�movxcij�� n�mo}�v�e�hkn�c�hkj'��hk�xrXc�¡Â|

� H � �°� 8 � 8 � � � = � � � = � � � �fX %��� H � ��� 8 � 8 � � � = � � � = � � � �fX X��

���

Page 12: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

Order = 1

Order = 2

Order = 33

211 2 3 4

5 6 7

8 9

10

1 2 3

54

6

��hk���imor ~�`�'gir&�imojseUeogimor�r���h ;8rXmor�c�e4nxmo�ir�mojUnx�$e�moh{vxci�����Õvxm$�Êcihkeor#rX�{r�}�r�c�e�jX��Ugir�mor�eogir �

�vxmor#e�g�r��knItXvx�ÅvxmorXv]t�nInxmo�ihkcÊv�e�r�j+v�ci� � �

� 9 � ��'vxmor#e�g�r��knItXv�e�hkn�cij

nx�$e�g�r#eomoh{vxci���kr+��r�mse�hktXr�jX��'gir��Êmoj�e �6n�mo�ir�m����kh{cirXvxm(��v�lilimon�yIh{}�v�eoh{n�c�� �ic�t�e�hkn�cij I �

v�mor�ps�ijse

I H � 8 � 8 � � �fX e�I � H � �fX ���I H � �

�fX ����'gir�jor�tXn�ci��n�ms�irXm'� �icit�e�hkn�cij�vxmor��

I H �°� 8 � 8 � � �X�°� 8 %�� 8 %�� � � �fX ��I � H ew�°� 8 � 8 � � � � �fX *��I H � �R% � 8 �q� �fX (��I � H e � � � � e ) �I � H e � � �°� 8 � 8 � � � � ei�q�I � H � � �R% � � 8 �q� �

� e`%���^%

Page 13: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

�+l�limon�yIh{}�v�e�hkci� �s¡Êvxjsh{j ��� �icit�eoh{n�c�j�nx�Åg�h{��gir�m�nxmo�ir�m�t�v�c�¡8r+r�vxjsh{�k|�xrXcir�m�v�eorX�;u¡i�Ie�h{c lim�v�t�e�hkt�vx�Ulimsn�¡i�krX}]jXu'm�v�morX��| vxmor ¡Êvxjsh{j�� ��cit�eoh{n�cij�nx�Àgihk��gir�m�n�ms�irXm]e�gÊvxceogimor�r���jorX�A�

���! ���� � � � � F ��� � � � � ��� � N%��� � � N � � ��� ��� N � �(� � N � � N%�&�����bdc nxmo�ir�m�e�n tXn�c���r�mse���rXmoh���v�e�h���rXj]� mon�} �knItXvx�'e�n �x�{n�¡Êv���t�nInxmo�ihkcÊv�e�r�j��ijsh{ci� e�gireom�vxcij�� n�mo}�v�eoh{n�c�hkc��)X %���v�ci� �fX X���u���r#msrXtXnx��cih{jsr

� H ������� � ������������ ������

� �� H ��

�� 8 � � � � 8 � � 8 � � 8 �

� �� � e X��

bdc�n�mo��rXm[e�n�t�n�c���r�mse#� mon�} �{n~t�v���tXn~n�ms�ih{cÊvze�rXj�uA��rvxt�eo�Êvx�{��| c�rXrX� eogir-h{c���r�mojsrnx���fe X���u��Ug�h{t(g�h{j

��� H ����� � 8 � � 8 � �� 8 � � 8 � �

� �� 9 � e e�

�Ugir�mor � H ��r�e�� H %W/Z�$moh{vxci���kr��+msr�v���+c]h{c�eorX��movx��nx�Av[� �icit�e�h{nxc]nE�xrXm�vÀeomoh{vxci���i�{vxm�r��{r�}�r�cÂe=hkc-e�gir'�knItXvx�itXn~n�ms�ih{cÊvze�r

j�|Ij�e�r�}�h{j�e�movxcij�� n�mo}]rX�fe�n-e�g�r��x�{n�¡Êv�� � 9 � t�nInxmo�ihkcÊv�e�r+js|~jseorX} ¡�|Y�Y�� � � 9 � � ] � ] � H Y�Y�� � � 9 � � ���ir�e�� ] � ] � � �

� e ������! ���� 3 F � _ � � � � ��� � � � � � � _ � � � � � ��� F N%����� � *IhkcitXr=��r�vxmsr�tXnxcijohk�irXmsh{ci��n�ci��|�vzyIh{js|~}]}�r�e�msh{t=limonx¡i�{r�}�j?�Uhkeogin���e�v � h{}���eogÊvx����vxmsh �v�eoh{n�c�j�h{c eog r �Êr��{� ��¡�rXtXvx�ijsr�n��'e�girfvxjsjo�i}]l�eoh{n�c n��+v�c r�yItXh�e(v�eoh{n�c t��imomsrXc�eh{ceogir NEP �ih{msrXt�e�h{nxc n�ci��|i��u�e�g�r���r�t�e�nxm-l8nxeorXc�e�h{vx�Kt�vxc ¡�r�t�n�cijohk�irXmsrX� e�n gÊv���r�n�cirt�n�}�l�n�cir�c�e B H � N P vxci� t�v�c ¡�r�mor�limor�jor�cÂeorX� v�jv�jst�vx�{vxm�� �ic�t�e�hkn�c � � � 9 + ����Ê�im�e�gir�mo}]n�mor�u�e�n�joh{}]li�khk� | e�gir h{c�e�r���m�v�eoh{n�c nx�[eogir ¡ivxjohkj]� �ic�t�e�hkn�cij]h{c tXh{mstX�i�{vxmt�|I�kh{ci��moh{tXvx�At�nInxmo�ihkcÊv�e�r�jXu���r��ir��Êc�r�v-cir�� l�nxe�r�cÂeohÕvx�A¡Êvxjor�� n�c�eogir#�ijo�Êv��$nxcirx�

��� H �� � 9 � e ����Ugir�mor ��h{j�eogir#m�vx��hÕvx�8�ih{j�e(vxcit�rÀ� mon�}�e�gir��{n�c���hkeo�i�ih{civx�*� + �UvzyIh{j���'gir��� "!�#*nx� B h{j'cinE���Umshkese�rXc vxj

� X

Page 14: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

.0/ B H � ��� N � 1 X% � � � = @ � �@ � ; 8 N V @ � �@ +�� �

� e ���4jsh{ci��e�g�r �icihkeor�r��{r�}�r�cÂe]msrXtXhkl8r�u���r v�lilimon�yIh{}�v�eor � � h{c e�r�mo}]j�nx�!�ÂcinE�Uc

¡Êv�joh{j�� ��cit�eoh{n�cij�� �irXjstXmohk¡8r�� l�mor��~hkn��ijo��|����Uh�e�gf�icE�ÂcinE�Uc���r�h{��g�e�j��� � H ����� 6 � � I � � � 9 + � �

� e *��*I�i¡�jse�h�e���eoh{ci� � e *���h{c�eon �fX��q��|~h{r��{�ij�eogir+�Êcih�e�r �6rX�krX}]rXc�e'}�v�e�msh�y�r �Â�Êv�eoh{n�cB � C���� ����� �� 8 576 B� V C� T ��� ����� �� 8 576 B� � C T V � ����� �� =? 576� D B I � C6������ ���%� �� 8 ���� ��� � � 8 , ����� ��� ? 576 B I C� � V � ����� �� 8 B I � C���� ���%� �� � e (���UgirXmsr B � CÅh{j B � C H B��>� �8C = B�� V V C = (e B I C = X % �8B�� V C = B�� V CÕ� �

��� ) ��'gir�tXn�}]l�n�cirXc�eU}�v�e�msh{t�rXjUvxmsr���r��Êcir��Rvxj�eogirÀ��n��k�i}]rÀh{c�e�r���m�vx�kj

B��>� �8C H %�� Y$Y @ I �@ + @ I��@ + � � ] � ] + 9 ���I�q�B�� V V C H %�� Y$Y @ I �@ � @ I��@ � � � ] � ] + 9 ��� %��B�� V C H %�� Y$Y I �

@ I��@ � � ] � ] + 9 ��� X��B I C H %�� Y$Y I � I�� ] � ] + ��� e�B I � C H %�� Y$Y I � I�� � � 9 ] � ] + ��� ���B I C H %�� Y$Y I � I�� � �� � ] � ] + ��� ���

��e

Page 15: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

B� V C H %�� Y$Y 1 X% � � I � I�� = � �W@ I �@ � I�� ; � ] � ] + ��� ��B� � C H 8 % � Y$Y @ I �@ + I�� � �� � ] � ] + ��� *��B� � C H 8 % � Y$Y I �

@ I��@ + � � ] � ] + ��� (��� � ) �

�'girRhkc�e�rX�xm�vx�kj�v�mor tXvxmomsh{r��Zn���e�nE��rXm�r�vxt(g eomoh{vxci���i�{vxm �Êcih�e�r�rX�krX}]rXc�e��ijsh{ci�v ��vx��joj �' ?rX��r�ci�imor �~�ivx�im�vze��imsr�vx�k��n�moh�e�gi} B �C2� *In�}]r��r�h{��g�e�j�vxci� hkc�e�rX�xm�v�eoh{n�cl�n�h{c�eoj;� n�m#��v��ijoj � ?rX��r�ci�imsr�hkcÂeorX��mov�e�hkn�c#vxmsr`limor�jorXc�eorX��hkc#eogir`e(vx¡��{rXj?hkc��+lil�rXci��h�ybsbob(�A@4nxeor e�gÊvze�e�g�r h{c�eorX��mov�e�hkn�cZl�n�h{c�eoj�vxmsrRvx�k��hkcZe�r�mo}]j�nx�#�knItXvx�UtXn~n�mo��h{cÊv�eorXj� 9 � � ����! ���� $ � � � � � _ � F ��� � � � N � � � � F � _ � � � �&� ��� � � ��� � � � N _ ��� � � � ��� � F ���� ��r�mÀe�gir]mor���h{n�c �Ugir�more�girt��imomsrXc�e���rXcijshked|R�xrXt�eon�m ���� �%� hkjÀcin�c � rXmsn � �UgirXmsreogirÀtXn�hk�8�Uhkci�ih{c���jUvxmor���u���r#vxjsjo�i}]rÀe�girÀt��imomsrXc�e��irXcijshked|�eon¡8rÀ�ic�hk� n�ms} � �4rXc�tXrxu��r�vxjojs�i}�r

� ��� � H IKUL J ��� 9 � ���q��Ugir�mor K h{jKe�gir4�{r�ci�xe�g�vxci� L e�gir�e�gihkt �ÂcirXjsj'nx�;e�g�r[tXn�hk�Ê�Uh{ci�ihkci��j�vxci� J �%� h{jeogir#tXn�hk�;tX�imsmor�cÂe4v�eUeoh{}]r[jseorXl�� = ���$�r�vx�kjon�cirXr�� e�n ��rXjot�mohk¡8r]e�gir�r<;8rXt�eoj�nx��e�gir�t(gÊvxci��hkci� }�vx��c�r�e�hkt��ÊrX�k�ij�n�c

eogir-��n���e(vx��rv�tXmonxjoj#e�girtXnxh{�2� F#hkmot(gig�nx�D0¿j �=n��ke�vx��r� Åv��Ghkj#�ijor�� eon �ir�jot�moh{¡�r-e�girjsrXmohkrXj,�, -" tXhkmotX��hke�� ��|�jo��}�}]h{ci��eogirÀ��n���e(vx�xrXj�vxtXmsn�jojUrXvxt(g r��{r�}�r�cÂeXui��r#gÊv��xr

cCbW= a b J =dc Z H ) 9 � � %���Ugir�mor cCb hkj�e�g�rÀt�vxlÊv�tXhkeon�m��xn��ke�vx��r�u c Z h{jKe�gir[�xn��ke�vx��rÀv�tXmonxjoj�e�g�rÀtXn�hk�Avxc�� a!bhkj�e�girÀr��Â�ihk��vx�krXc�e'jor�mohkrXj'mor�johkjse(v�citXr#nx�Åe�g�r�Êmohkci�-tXhkmotX��hke#� h{cit��{�i��h{ci��t�n�h{���Uh{ci��h{ci�

msrXjohkjse�vxcitXr����D$�r�tXvxc�morX�{v�e�r[eogir#t�vxlivxtXh�e�n�m��xn��ke�vx��r[e�n-eogir#tX�imsmorXc�e��Uhkeog� �cCbA8 J H ) �

� � X��� h{j�eogir#t�vxlivxtXh�e(vxcit�rÀnx�$e�gir+�Êmsh{ci�t�v�lÊvxtXh�e�n�m�����

Page 16: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

�$n>�ici� c Z uK��rfcirXr�� eon�tXn�cijsh{�ir�m�e�gir��xrXt�eon�ml8n�e�rXc�eohÕvx��� nxmo} n��+�wvxmovx�Êv�| 0Çj Åv��#�c Z H 8 Y b @

� P@ED ] K � � eÂ��Ugir�mor�e�gir�lÊv�e�g nx�Uhkc�e�rX�xm�v�eoh{n�c��]h{j�e�v �xr�c vx�{n�c�� e�gir��Uhkci�ihkci��jX� �'g�h{j-�{hkcir

hkcÂeorX��movx��hkj[h{c�tXn�c���r�cih{r�c�eÀe�n�t�v�moms| n���e#�ihkmor�t�e���|�u;jsn���rt�n�cijseomo�it�e�vxc�r �Â�ih��xv��{rXc�er�y�l�morXjsjohkn�c�e�gÊv�e�h{j�r�vxjsh{rXm�e�n�r��xv��{�Êv�eor+hkc�e�gir[� E . lÊvxmovx�ih{�x} �*bdc�jogin�m�e�u~��r�Êc��eogir#v���rXmovx��r[�xrXt�eon�mUl8n�e�rXc�eohÕvx�8h{c�e�g�rÀtXn�hk�Amor���h{nxcfvxci�;uÊvz� e�rXm�r���vx�{�iv�e�hkci��e�g�r[e�h{}]r�ir�moh��xvze�hk�xrxui}��i�keoh{li��|�¡�|�eogir#�{rXc��xe�gfnx�$e�girÀ�Uhkci�ih{c��iuI�~h � �

c Z H28 K b� K �)% � L = L � �ZY 6

" � �Y " @ � �@ED � �� � ] � ] + 9 � � ����Ugir�mor �#h{j*eogir�hkcicirXm�m�vx�ihk�ij�n���eogir�t�n�h{�Ivxci� L h{j*eogir�t�n�h{�Âe�gihkt �ÂcirXjsj+� mor�l8rXv�e�r��

gir�mor�� n�mtXn�c���r�cih{r�citXr���� @4nxeor�eogÊv�e]e�gir �irXcinx}�r�cÊv�e�nxm�nx�+e�gir�r�yIlimsrXjojsh{n�c eogÊv�elimsrXt�rX�ir�j e�g�r�hkcÂeorX��movx�[hkj�ps��jsefe�gir���nx�{�i}]r nx��eogir�tXn�hk�2� �4r�citXr�u[e�gir m�vze�h{n n��eogir�h{c�eorX��movx� �Â�Êvxc�eohked| vxci� e�gir�tXn�hk�$�xn��{�i}]r�hkj4e�g�rvE�xrXmovx��r���vx�{��r�nx�=e�g�r���rXt�e�n�ml�nxe�r�c�e�hÕv����Uhkeogih{cReogir�t�n�h{��morX�xh{n�c;�-�'g�r]l�mon~�i�it�e�nx��e�gihkj[�Uhkeog�eogir]tXn�hk���Uh{ci��h{ci��krXci�xeog;u,��h���r�jv tXn�c��xrXcihkrXc�e �Êcihkeor �6rX�{r�}�r�c�e�mor�limor�jor�cÂe�v�e�hkn�c nx�'e�g�r��{h{c�r�hkcÂeorX��movx�hkc ��� e����:$�r�t�n�}�l���e�r�eogir��krXci�xeogRnx�`eogir��Uh{c��ih{ci���ijohkci��e�g�r�� n�mo}�vx�kh{jo} h{c>*Ir�tx�X�� %I� %�e�gÊv�e'|~hkrX�{��j

K b H % � I 1w� � = ] � = � I � 8 �q� � Xe ] ;:9 � � ���jo��t(g�e�gÊvze I h{j`e�g�r�eonxe(vx�ÊcÂ�i}�¡8r�m�nx�8e��imscij�hkc]eogir�tXn�hk�Ê��hk�xrXc�¡�| �)% ��`vxci� I �hkj�e�gir#cÂ�i}�¡�rXmUnx�*tXn�hk�;�Õv�|xrXmoj'� msn�}&�)% ����'gir�tXn�hk�$msrXjsh{jse�vxcit�r�t�v�c vx�{jsn�¡�r�rXvxjohk�k|fr�jse�hk}�vze�rX� v�e�e�gihkj4l�n�h{c�eX�,�#h���rXc�e�gir

�Uhkmor'tXmsn�joj �djsrXt�eoh{n�civx�Êvxmsr�v � ] �Kvxci�tXn�c��i�it�eohk�~hked| ? b ��� �

( � /�� ) � * ��tX} � n�m`tXnxlil8r�mXu��

X / � ) � * ��tX} � n�m'johk�k��r�m(��uie�girÀ�Uh{c��ih{ci�-msrXjsh{jse�vxcit�r�hkja b H K b� ? b ] � �

� � ���Àn�h{ci��¡Êvxt � eonfeogir-tXnxh{���xn��ke�vx��r�hkcÂeorX��movx��hkc ��� ����uA��r]r���vx�{�Êvze�r-hke[�ijohkci��e�gir�Êc�hke�rÀr��{r�}�r�cÂeU}�v�eomoh{t�rXjUvxjc Z H 8 K b� K �R% � L = L � � � D Â� ��� B I C�� ���� ��� 8 ���� ��� �

� � *��� �

Page 17: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

�Ugir�mor Â� �hkj[v��xrXt�eon�m�Ê�k�{rX���Uhkeog ��� ��j�� n�m4eogir-�irX�xmorXr�jÀnx�`� mor�rX�inx} �Uh�e�gihkc e�girt�n�h{��vxci� � ) �xj`nxe�gir�ms�UhkjorUvxci�n�c��k|�tXn�}]li��eorX�-� n�m�eomohÕv�ci���i�{vxm*r��{r�}�r�cÂeoj`lig�|~joh{tXvx�{��|� n���ci� �Uhkeogih{c e�gir�tXn�hk�K�xn��{��}�r ��nxeogirXm��Uh{jsr�rXmsmon�msj��Uh{�k�=morXjs�i�ke(���� � � johk��cih��irXj�veom�vxcijsl8nxjor#n�l�rXm�vze�h{nxc;�

���! ���� 3 � F � �#N%�� � � � � ���&��� � � � � �bdc�e�gihkj#h{cih�e�hÕv��*��n�m��wu*��r]rXc�� n�mstXr��vxcih{jsgih{c�� �[hkmohkt(gi�{r�e#¡8n���ci�Êvxm�| tXn�c��ihkeoh{n�cij#n�cvx�k�Ar�yIeorXmscÊvx�Å¡8nx�ici�Êvxmsh{r�jX�`�'gihkj�hkj'r �Â�ih��xv��{rXc�eUe�nr�citX�kn�johkci�-e�girÀ��nx�{�i}]rÀh{c�v-l8r�m �� r�t�e4rX�{r�t�eomoh{tÀt�n�ci�i��t�e�hkci��r�citX�kn�jo��morx��bdc eogir�� �Ie��imsrxu�v]jsl8r�tXh{vx� �sn�l�rXc��]¡�n��ici�Êv�ms|t�n�ci�ih�e�h{nxc��Uh{�k�8¡�r[hkcitXn�msl8nxm�v�eorX��eon�johk}��i�Õvze�r4eogir[r ;Ar�t�e�j'n��$eogir[n�l�rXc�msrX��hkn�c�� h2�¿rx��Uh�e�gin��Ie�vxc�|�rXcit��{n�js�imor��&B e C1����! ��#"�� � � � � F ��� � � �&� � ' �(� � � ' ��� � �&� � � _ � � _ F ����� ��'gir . vqyI��rX�k�ijseomor�jojKh{cvxc]vzyIh{j�|~}�}]r�eomoh{t�mor���h{n�c��Ug�rXmor�vÀ}�vx��cir�e�h{t �ÊrX�k�-h{j`�in�}��hkcÊvxc�e ��r��{rXt�e�msh{t �Êr��{� r<;8rXt�eoj�tXvxc ¡8r�h{��c�n�mor��w��vxci� h{j-�ir �Êcir��Z¡�| v movx�ih{vx��vxc���kn�ci��h�e��i�ihkcÊvx��tXn�}]l�n�cirXc�eUhkc v-msrX��hkn�cfn���e�jsh{�ir#nx��v-l8r�mo}]r�vx¡��{rÀ¡�nI��|�h{j��

� H �576 ��� � ����V 8 ��� � � V � �� ��� V � � � �� 8 � �V �

���� � � (��

�'gir#� n�mot�rÀn�cfe�gir#limsnzpsrXt�e�h{�krÀh{j'��h���r�c ¡�|

� H Y�����

. [ � ] c �� ) ��Ugir�morfe�gir�h{c�e�r���m�vze�h{nxc h{jt�vxmsmohkrX� n���e]nE��r�m]eogir��xn��{��}�r�eogÊv�e]h{cit��{�i��rXj-e�gir

limsnzpsrXt�e�hk�{rx� � �'girfjohkci���{r�hkc�e�rX�xm�vx��hkci�ihkt�v�eorXjvRe�msh{li�kr�h{c�e�r���m�v���nE��rXme�g�rf�xn��{��}�rgir�mor��¨� ��joh{c�����vx��jojD0¿j�Õv��#u`��rftXvxc morX���itXr�e�g�r���n��k�i}�r�h{c�e�r���m�vx��e�n�v jo�im���vxtXrhkcÂeorX��movx�=� �Ugih{t(g�h{j'rXvxjohkrXm�e�n]r���vx�k�Êv�eorE���

�\H Y� � ��� � [ � ]�� �� I�q��Ugir�mor � hkj4v]�icih�e��xrXt�e�n�m�e�gÊv�e�l�n�h{c�eoj�nx��ed��v�mo� � msn�} e�g�r�jo��ms��vxt�r�js�imomsn��ici���hkci��e�gir-l�monzpsr�t�e�hk�{r-v�ci� e�gir-hkcÂeorX��movx�,hkcRe�gihkj[t�vxjsrh{j#v��in���¡i�{r-hkcÂeorX��movx��nE�xrXmÀe�gir

t�|I�kh{ci��moh{tXvx�Ajs�ims��v�tXr���jsrXrXc h{c���hk���imor&*����*IhkcitXr,��r�v�mor`n�ci��|+hkc�e�rXmsrXj�e�rX��h{cÀeogir`�{n�c���hkeo�i�ih{civx�z� nxmotXr�� e�gÊvze?�Ugih{t(g#��r�cirXmov�e�r�jvxt�tXr��{rXmov�e�hkn�c�nx�$e�gir#limsnzpsrXt�e�hk�{rxuI��r�t�vxcf�Umoh�e�r

��

Page 18: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

��hk���imsr *��$��r�t�vxl�nx�$e�gir#hkcÂeorX��mov�e�hkn�c�lÊvze�g;�

� � H % � ���576� � ����Y� � � �� � ��� V���� V� ] + =�576 V�Y 6 � � �� 8 � �V � ��� � � � �� � ] � 8 �576 V�Y 6 � � �� 8 � �V � ��� � � � �� � ] � �� %��

�Ugir�mor +��6 vxci� +�� vxmor�eogirl8nxjohkeoh{n�c�j+nx�Ke�gir-�kr�� e�vxc�� msh{��g�eÀr�ci�ij#nx�Ke�gir-t�|~�{h{c��irXmeogÊv�eK�irXjstXmsh{¡�rUeogir�h{c�e�r���m�v�eoh{n�c-js�ims��v�tXr4v�e=e�gir�vxms}�v�eo�imor'j�e(vxm�e�hkci��l�n�jshke�hkn�c + H ) ��'gir�jor�hkc�e�rX�xm�vx�kj*v�morKr���vx�{�iv�e�r����ijsh{ci�*Ih{}]lijonxc 0Çj*mo�i�kr=joh{c�tXr�eogir���vx�k�irXj$nx�ieogir �irX�{�nE��r�m[e�gir-js�ims��v�tXrnx�=e�gir-t�|~�{h{c��irXmÀv�mor���r�cirXmovx�{��| ��rX�k� �6¡8r�gÊv���rX�A� � e�gir�mÀ}�r�e�gin~�ijtXvxc ¡�rR�ijor�� �Uhkeog ��n~nI� morXjs�i�keojX� b6e�h{j�h{}]l8n�m�e(vxc�ee�n�e(v ��rRrXcinx�i��g l�n�h{c�e�j]h{cmsrX��hkn�cij+�Ugir�mor�eogir �ÊrX�k�R��vxmohkrXj[movxlih{���k|�� *Inx}�r�� nxmo} nx��vx�Êvxl�eohk�xr�h{c�e�r���m�vze�h{nxcRh{jmsrXtXnx}�}]rXci��rX�;�

� *

Page 19: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

���! ��#"(" $ � � � � F � _ � � � ��� � F � ��� � _ ��� � � � � � N%��� � ��� F N%����� � bdcZeogih{j�}�n~�ir��2u�eogir t�h{mot��ihke �M�Êr��{�Zr��Â�Êv�e�hkn�cij�vxmor jon�����rX� hkc v msh{��nxmon��ij]johk}��i�{vM�e�vxcirXnx�ij�}�vxcicir�mX���'gir�r �Â�Êv�eoh{n�c�j�vxmsr)��joli�khke � vx�kn�ci��e�gir�}�r�t(gÊvxcihkt�vx� �dr��{rXt�e�msh{t�v���ih��~h{�ir�js�it(g eogÊv�ee�gir�vxms}�vze��imsr���rX�knIt�hked| h{j-r���vx�k�Êv�eorX� �Uhke�g�h{c e�gir���yIr����dl�n�h{c�eh�e�rXmov�e�hkn�c-vxc���vÀ}]h�yIrX�?E`�i�{r�m`e�h{}]r�j�e�rXl�lih{ci��jot(g�rX}]r�� h{}]li�{hktXhkeÅ� n�m �irX�{���vxmoh{vx¡i�krXjvxc���"�m�v�cE� � @4hktXn��kjon�c� n�mKtXhkmotX��hke=��vxmoh{vx¡i�{r�j(�`vxci�]e�gir4vxms}�v�eo�imorUl�n�joh�e�hkn�c�hkj=�ir�eorXm �}]h{cir����ijohkci� vfjor�}�h �dhk}�li�kh{t�hke E`�i�{r�m#eoh{}]r �6jse�r�lilihkci�fjot(gir�}�r����'gihkj�hkjÀcirXt�rXjojovxms|¡�rXtXvx�ijor�e�gir�e�gir�cir�� vxmo}�v�e���morUl8nxjohkeoh{n�chkj��ijsrX��eon���r�cirXmov�e�r4v�c�r�� }]rXjogA�,�'gih{jlimsrXt��{�i�ir�j-e�gir��ijsr n��4hk}�l��{h{t�hke#e�hk}�r �dj�e�rXl�lih{ci�R� nxm�e�girfl�n�joh�e�hkn�c;���w��mse�g�rXmo}]n�msrxuhkc n�ms�irXme�n�limor�jor�ms��r e�gir js|~}�}]r�eoms| nx�+e�gir �Êcih�e�r�rX�{r�}�r�c�e�j�|Ij�e�r�} uUv jol�rXtXh{vx�jsli�{h�eoe�hkci��hkj'�ijor�� e�njsrXlÊvxmov�e�rÀeogir#tXh{mstX�ih�eUr �Â�Êv�eoh{n�c�jU� msn�} eogir+�ÊrX�k�fr �Â�Êv�eoh{n�cij��

��e+eogih{j4l8nxh{c�e�uÊ��r�n���eo�{h{c�r�eogir�j�|Ij�e�r�} r �Â�Êvze�h{nxcij-�°�q�4�À���x��h{c�e�gir�h{m��ih{jstXmsr�e�r� n�ms} vxj

��������

B � C =���� �� � B I � C 8 � � �Z � ��� ) �� Z�� � " � � � � � Z � � ��� � � a � ) � 8 � � � �

���������

�������� �������

���� �%� � � J �%� � � c ��� � �

� ��������������H

��������

��� �� � B I � C ) � ) �� Z�� � " � � � � � Z � � ��� � 8 � a 8 � ) � � � � �

���������

�������� �������

���� �J �c �

� ��������������=

��������B� &� C B� V C 8,? 576 , ��B� � C � ) � � ) � � ) � � ) � � ) � � ) � �

���������

�������� �������

T V � �%� �

T ��� �%� �

���� ��� �

� ��������������

�� X���Ugir�mor , ��h{j�eogir#limonqpsrXt�eoh{�kr[��rX�knIt�hked| ��h{c�eogir � �d��h{mor�t�eoh{n�cw��vxci�

) � H������ �����)) ���)

� ���������� 9

�� e�� (

Page 20: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

��� H B I CÂ� � �� ���vxci��� h{jvxc hkcÂeorX��r�m-h{ci��r�y �Ugihkt(g hkci�ihkt�v�eorXj�e�g�r�cÂ�i}�¡8r�m-nx�4eogirfcin�ci�kh{cirXvxm

h�e�rXmov�e�hkn�c���� = ��h{j`e�g�r4cir�� �s����rXjoj�����r�cirXmov�e�r���¡�|-e�g�r4cinxc��d�kh{cirXvxm,hkeorXmov�e�hkn�cw��vxc����vxj[h{c��ih{tXv�e�r��Rlimor��~h{n��ijs�k|�� � hkj4eogir�e�hk}�r�jseorXl � �Ugir�mor � = �-h{ci�ihkt�v�eorXj�e�gir-cir��eoh{}]r[jseorXlf��r�vxmor#jsn��k�~h{c���� n�m(���b6e�h{jKh{}]l8n�m�e(vxc�e`eon�morXvx�{hkjor'e�giv�e�eogir�js|~jseorX}�h{c �� X��`h{jKv #�������!Àjs|~jseorX}P�UgirXmsr

��rÀgÊv���r#tXnxcitXr�cÂeom�v�eorX�fe�girÀc�n�ci�{hkcir�v�m�js|~j�e�rX} limon�l�rXm�e�hkrXj�hkc�e�girÀmsh{��g�e �6gÊvxci� �djohk�irnx�,�� X����3$ r�jse�vxmse=�Uhkeog]vxc�hkcihkeohÕvx�~���ir�joj�� H ) � nxm,e�gir'��r�t�eon�m�l�nxeorXc�e�h{vx�2u�t��imomsrXc�e�utXvxlÊvxt�hke�nxm[��n���e(vx��r]vxc���e�g�r�limsnzpsrXt�e�hk�{r-��r��{n~tXhked| vxci� h�e�r�m�v�eor 0¿monx�ici��vxc hkcÂeorXmscÊvx��knIn�l �ic�e�hk�*e�g�r�jon��k��e�hkn�cRr�momonxm[h{j4�{rXjsj+e�givxc jon�}]r�jsl8r�tXh��irX� ��vx�{�ir��À�'gir-jonx�{��eoh{n�cvx�k��n�mshke�g�} hkjfh{�{�k�ijseom�v�eorX� hkc joh{}]li�kh��Êr�� =ÊnE�4�dt(gÊvxm�e � nxmo} hkc ��h{����mor>(�� b6e�t�v�c¡�r jsrXr�c e�gÊv�e]e�g�r cin�c��{h{c�r�vxmjonx�{��eoh{n�c t�vxcZ¡8r�t�vxmsmohkrX� n��Ie��Uh�e�gin��Ie�gÊv��~h{c���e�nmsrX��r�cirXmov�e�r4vxci�]��vxt�eon�m,e�gir��{r�� e �6gÊvxci���6johk�ir'}�vze�mohÎy�� n�m=rXvxt(g�h�e�rXmov�e�hkn�c;� � cir4c�rXrX��jeon�msrX��r�cirXmov�e�r vxci� ��v�t�e�nxm]eogir � * }�vze�mohÎy n�c��k| n�cit�r rXvxt(gZeoh{}]r�j�e�r�l;� �'gih{jjsl8r�rX�ij��il eogir jsn��{�Ie�h{nxc ��m�vxj�e�h{tXvx�{��| nE�xrXm�eogir��ijo�Êv���msrX�k�it�e�vxcitXr �d¡Êv�jorX�Zjon�����rXmsjX��Ê�im�e�gir�mo}]n�mor�u;e�gir���yIrX� �dl�n�h{c�e#jonx�k��r�m#gÊvxj�vf�Uhk�irXmÀmovx�ihk�ijÀnx��tXn�c���r�mo��r�citXr�e�gÊvxceogir @4r��'eon�c��'�4vxl�gijon�c�}]r�e�g�nI��vxci��h{j'jsh{}]li�{r�m�e�nhk}�li�krX}]rXc�e��

� c ��vxt�e�n�msh{johkci�e�gir��{r�� e �dgÊv�ci���djsh{�ir�}�v�e�msh�y8��n�c�r��Uh{�k�?cinxe�r�e�gÊvze+e�g�r�jonx�{��eoh{n�c� n�mKe�gir � = �[eoh{}]r+jseorXlfmor��Â�ih{msrXj�eogirÀjon��k��e�hkn�c�n���v�cin�cij�|I}]}]r�e�msh{t[j�|~jse�r�} �=�'girjs�i¡i}�v�e�msh{tXr�j(B � C=vxc�� B I � CKvxmsr�Õvxms��rxu?j�|I}]}]r�e�msh{t�u?l8n�jshkeohk��r�ir �Êcih�e�r �R* ���#�[vxc��jslÊvxmojsr[�Ugih{�kr4eogir[�{nE��rXm�js�i¡i}�v�e�msh{t�rXj�eogÊv�e'�ir�jot�moh{¡�r+eogir[tXhkmot��ihke�vxmor[c�n�cijs|~}]}�r�e �msh{tx�*b6eK}�v ��rXj=jor�cijor�e�n#jor�lÊvxmov�e�r'e�g�r�j�|~}�}]r�eomoh{t�u�l8nxjohkeohk�xr �d��r��Êcih�e�r'lÊv�mse=� mon�} e�girhkci�ir��icihkeorxuÂcin�cij�|~}�}]r�eomoh{tUt�h{mot��ihkeKr��~�iv�e�hkn�cijX� $�r�t�vxc��in�eogih{jKhk����r4mor��Umohkeor��� X��vxj�v-��r�cirXmsh{tÀlÊvxm�e�h�e�h{nxcih{ci���

���

B � C �� ��� � � B � C

����

��� ��� � �

� ���� H

��� ��� � �

� ����

�� ����'gir * ��� �Êcih�e�r`r��{rX}]rXc�e*}�vze�mohÎy[hkjÅtXn�c�e(v�h{cir���hkc�eogir @ @Uy @ @ }�v�e�msh�y B � C8��@ @

hkj4e�g�r�cÂ�i}�¡�rXm[n��=�irX��msrXr�jÀnx�,� mor�rX�inx} hkc e�gir �Êcihkeor�r��{rX}]rXc�e+}�r�jogw��u8e�g�r�tXhkmotX��hketXvxlÊvxt�hke(v�citXrUvxc���msrXjohkjse�vxcitXrUe�r�mo}]j`h{c-e�g�r %Ey %[}�v�e�msh�y#B � C1���'gir @ @'yE%#t�h{mot��ihke �6eon �t�n�h{�~tXn���li�{hkci�[jo��¡i}�vze�mohÎy�h{j,��h���r�c-¡Â| �� ��vxci��e�g�r�%qy @ @ t�n�h{� �6e�nM�dtXhkmot��ihkeÅt�n��ili�kh{ci�js�i¡i}�v�e�msh�y�hkc �� � � ui�Ih � �

B�� C H B � C = ? 576� D B I � C �� ��% )

Page 21: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

Is error

Tolerancelower thanin A,V,I

and build new FE system

Generate new mesh

Increment time step

Factor FEM matrix

Evaluate material magnetisation

Solve for updated guess

for A, V, I

Compute Force

Compute new velocity and position

coil?exited

armature

Has

No

Yes

Exit Simulation

Go for another iteration

No Yes

Go on to computenew armature

speed and position

Set initial values for A, I, V, u, zTime step=0

Build initial FE system

��hk���imsr (������knE�Gt(gÊvxm�e�hkci�ihkt�v�eoh{ci��e�g�r�}]n�jse�hk}�l�n�mse�vxc�e#jseorXlij�h{c�e�gir]cin�ci�kh{cirXvxmjsn��k�xrXm�vxci��e�hk}�rÀhkc�e�rX�xm�v�eoh{n�c�msn���eoh{cir��

�� � H � 8 � � �Z � ��� ) ��� �� *���� ��� H ��� ��

� Z�� � " � � � � � Z � � ��� � ) � �� ����

�� (��B � C H ��

� � a �

8 � � � ����� � * ) �

��| l8r�ms� n�ms}�hkci��v�jsh{}]li�{r�jo�i¡ij�e�h�e���eoh{n�cR� n�m � � e�gir��icE�ÂcinE�Uc �xr�y~e�nxm�l�nxeorXc��eohÕvx�Õ��u���r+t�v�c�mor��i�it�r��n�mC�st�n�ci�ir�cijor �Â�=eogir+r�cÂeoh{msr,�Êr��{��jon��k��e�hkn�c�hkc�e�n�v�js|~j�e�rX}�h{ceorXmo}]j'nx�$e�girÀed��n�t�h{mot��ihke��xv�mohÕv�¡i�{r�j�n�ci��| ��t�n�c�e(vxhkcirX�fh{c � � ��� �4rXc�tXrxu

�8B�� C 8 �� ��� B�� C � �� ��� � � H � � 8 �� ��� B � C � � � *��q�%I�

Page 22: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

vxci�� H B � C � � � 8 �� � � � �

� * %��� citXr�e�gir �imojse�js|~jseorX} � *��q�#h{j�jsn��k�xrX� ��joh{c�� vxc�* ��� jonx�k��r�m��{h��xr "�gin��krXj���|

��vxt�e�n�msh{jov�e�hkn�c�n�m'e�gir "�n�czps����v�e�r �Àm�vx�ihkrXc�e . r�eogin~�;uÊe�gir�cir�� �x�irXjsj4� n�m'e�g�r��xrXt �eon�m=l8nxeorXc�e�h{vx�Êt�v�c�¡�r�� n���ci���ijsh{ci�#e�g�r4jsrXtXnxci��r�yIlimsrXjsjoh{nxc�h{c ��* %x���U� �'gih{jKlimonqpsrXt�e�ijsrX��v�"�gin��krXj���|���v�t�e�nxmoh{jov�e�hkn�c;uz¡8r�t�vx��jorUhke`hkj���vxhkmo�k|�r��t�h{r�cÂe`� nxm I I�� � ) ) ) ) n�mjsn�vxc��;uÂn�citXr B�� Cwhkj,��vxt�eon�mor��;u�e�gir'��vxt�e�n�m`tXvxc�¡�rUmor��ijor���� n�m,e�g�r��Iy�r���l�n�h{c�e=h�e�rXmovM�eoh{n�c;u�eogirXmsrX¡�|]vx}]n�mseoh{jsh{ci�+eogirUe�h{}]r�t�n�jseKnx�8��vxt�eon�mohkj�v�eoh{n�c�nE�xrXmKjor��xrXmovx�8h�e�r�m�v�eoh{n�cij���UrXl�r�v�eorX��jon��k��e�hkn�cij��Uh�e�gf�ih ;8rXmsrXc�eUmohk��g�e �6gÊvxci���6johk�irXjUvxmsrÀ��rXm�|���vxjseX�¨�b6e`hkj,h{c�e�r�mor�jse�hkci�+eonÀcinxe�r�e�gÊv�e�e�gir�eoh{}]r�j�e�rXl�lih{ci�[� nxm*e�g�r'}�vx�xcir�eoh{t=��rXt�e�n�m`l�n �

eorXc�e�h{vx�Ajsn��{��eoh{n�c�h{j�¡ivxjor���nxc�� �i�{��|�hk}�l��{h{t�hke������ D ��¡Êvxt ����vxmo� � E`�i�{r�m'h{c�e�r���m�vze�h{nxc;��'gihkjÀh{jÀt�n�c���rXc�h{rXc�e�¡�rXt�v��ijor��rgÊv��xreogirt�vxjsr-�UgirXmsreogir-}�v�e�r�mohÕv���tXnxci�i�it�e�hk� �h�ed| ��vxcihkjogir�jÀvxci� eogir���r�t�eon�mÀl8n�e�rXc�eohÕvx�*h{j+��rXjot�mohk¡8r�� ¡�|Rvxc rX�k�{h{lIe�h{t��f $v�li�Õvxt�r�n�m�$n�h{jsjon�c��6�{h��xrE� ��� E v�cÂ| �sr�y�l��{h{t�hkeocirXjsj ���Uh{�k�Å�{r�v�� e�n���cicirXt�rXjsj�vxm�| ¡8n~n �`�xr�rXlihkci�i�� c e�girfnxeogirXmgÊv�ci�;u=e�girftXhkmot��ihke-��vxmshÕvx¡i�krXj��Ie�h{�kh{jsr�v�"�m�vxcE� � @4h{t�n��{jsn�c e�hk}�r�hkc��eorX��mov�e�hkn�c�jot(gir�}�r����'g�r�morXvxjonxc � n�mÀe�gihkj�hkjÀe�gÊv�e�e�g�r�}�vxh{c�r�cirXms�x| r�yIt(gÊvxci�xr�h{jr�y�l�morXjsjor��-h{cÀe�r�mo}]j$n��itXnxh{��tX��momor�c�e�j*vxci��tXvxlÊvxt�hkeon�m;��n���e(vx�xrXjX�$�'gir�}�v�eorXmshÕvx���{n�jsjorXjvxmsr�jsrXtXnxci�Êvxm�|�r<;8rXt�e�j,eogÊv�e,��rXl�rXci�n�c�eoh{}]r �6m�v�eor �dn�� �dt(gÊvxc���r=nx� �ÊrX�k��n�m-�~hkcirX}�v�eoh{t��vxmshÕvx¡i�krXj`v�ci�;u�gir�citXr�u�vxmsr���rXv �xr�m=r<;8rXt�eojKeogÊvxcrx�¿�i��u�tXn�hk���Uh{c��ih{ci�À�kn�jojsrXj���v�e=�{rXvxjsen�c }]n�j�e[�ijsr�� �i��eoh{}]r�jst�vx�krXj����#b6eÀjog�n��i�{� ¡�r�jovxh{� eogÊv�eÀjsgin�m�e�rXm4e�h{}]r�jot�v��{rXjÀ}�v�|msr �Â�ih{msr#}�n�msrÀmohk��n�monx�ij'vxjsjo�i}]l�e�hkn�cij'n�c�}�v�e�r�mohÕv��A¡�rXgÊv��~h{n���mX�

$�rÀvx�{jsn�gÊv��xr[e�gir4r<;8rXt�eoj'nx�?e�g�r+tXnxcÂ�xrXt�e�hk�xrÀe�rXms} , � ? 576 @ ��� @ + ui�Ug�h{t(g���h���rXjmsh{jor�e�n�h{ci�i��tXrX��t��imomsrXc�e�j�n�c�e�g�r[vxms}�v�eo�imor��,�'gihkj�e�r�mo}Ph{j�vx�{jsn�v�msrX�{v�e�h���rX��|���r�v �r ;Ar�t�e�uIjon���r[�ir�tXn��il��{r[h�e�t�n�}�l��{r�eorX��|-� mon�} e�g�r�Âh{cir�}�v�eoh{tUjonx�{��eoh{n�c;�3$ r[vxjojs�i}�reogÊv�e�e�gir�eoh{}]r#jse�r�l t�vxcRvx�k��v�|Ij+¡8r�}�vx��r�js}�vx�k�ÅrXcin�����g e�n�vx�{�knq���ij+eon��ijsr�e�gir�xrX�{n~tXh�ed|]h{c�eogir+l�morXt�rX�ihkci��e�hk}�rUj�e�rXl�eon�tXnx}�li�Ie�r4eogih{j=e�r�mo}��,bdc�t�v�jorXj��UgirXmsr+e�girhkcitXmsrX}]rXc�e(vx�$t(gÊvxc���r�h{c���r��{n~tXhked|�hkj �s�{vxmo��r ��hkc v]eoh{}]r�j�e�r�l t�vxc hkcÂeomon~�i�it�r�jonx}�rr�momonxmX�`bdc�e�gir[��n�msjseUt�v�jorxuieogih{j�t�vx�ijsrXj'e�g�rÀlimonzpsr�t�eoh{�{r[vxtXt�rX�{r�m�v�eoh{n�c�e�n-¡�rÀjo�{hk��g�e���|nE��r�mor�jse�hk}�vze�rX��h{c�eogir��~hkcirX}�v�eoh{t[jsn��k�xrXmX��'gir&�Âh{cir�}�v�eoh{t[jsn��{�Ie�h{nxc�h{j'��r�cirXmov�e�r���� msn�} e�g�r��kh{cirXvxm�j�|Ij�e�r�}���

� )8#� � D �

� ��

��� �� , �%� + ��� � ���� H

���� )� � D �

� ��

��� �� , �+ �� ���� =

��� ��� � � !#")

� ����� D � * X��

�'gir �ÂhkcirX}�v�e�hkt�eoh{}]r#jse�r�lilihkci���ijsrXj#v "�movxcE� � @�h{t�n��{jsn�cRjot(g�rX}]r��UgirXmsr � � h{jvxc r�y~e�m�v�l8n��{v�e�r��Z� n�mstXrR�ijsh{ci� eogirRlimsrXjsrXc�e�tXn�}]li��eorX� � n�mstXr vxc�� v lÊvxjse��xv��{�ir

% %

Page 23: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

� n�m�� n�mot�r��ijsh{ci���kh{cirXvxm4r�y~e�m�v�l8n��{v�e�hkn�c;� E=}]li�knq|~hkci��� n�mstXr�r�y~e�m�v�l8n��{v�e�hkn�cRv�ci�Re�gir"�movxcE� � @�h{tXnx�{jonxc�msrXt�h{l�r[e�n-e�gir+�Êmsjse�monE��nx�'� * X���|~h{r��{�ij� � H �% �)X � �%� 8 � � � �

� * eÂ�@4��}�r�moh{tXvx�`r�yIl�rXmsh{}]rXc�e�j�h{ci�ihkt�v�eor-e�gÊv�e�e�g�h{j#|IhkrX�k�ij�jsn��{�Ie�h{nxcijÀ�UgirXmsr�js|~jseorX}r�cirXms�x|�h{j'¡�r�ese�r�m�t�n�cijsrXms�xrX� eogÊvxc�hk� � ��� n�ci�k|���r�mor��ijor��;� ��/ � ����!&+�� E ��!F�#��7 �9����(�* 7 ��2"�:��!"�#� 4 * ��(�� ����ED7 *?�,��� �.� !&>60

!"��� �?!F���?�.!&���9��AC�#2F��������!���#" � �� ��� � � �� jsh{�kh{tXnxc�tXn�c�eomon��k�{rX��morXt�e�h �ÊrXm'j��Uhke�t(g�rX�f�imoh��~h{ci��t�h{mstX�ih�e'�{n~n �Âj�jst(girX}�v�e�hkt�vx�k�k|]�{h��xreogir#�ihÕvx�xm�vx}�h{c���hk���imor�� ) �

when V <0c

Vc when V > 0c

Launcher

Vl

coil

Moveable core

+C

current I

series resistance)(including coilR

Loop

Loopcurrent I

Triggerpulse

��hk���imsr'� ) �#*E"4� �Êmsh{ci�Ut�h{mot��ihkeX� @4nxeor=eogirK�ijorKnx��vU� msrXr �2�UgirXr��{hkci�U�ih{n~�ir,e�n�limsr���r�c�emsr���r�mojsr�t(gÊv�mo��hkci�nx��eogir#t�vxlÊv�tXhkeon�mX�

�'gir�tXvxlÊvxt�hke�nxm � hkj�t(gÊvxms��rX� eonRe�gir��Êmohkci�R��n���e(vx�xr c 6 � $ girXc e�g�r���v�eor�h{jeomoh{�x��rXmsrX�;u�eogirÀ�ihknI�irÀhkj'mor���rXmsjor �d¡ih{vxjor��Rvxci��eogir#tX�imsmorXc�e =ÊnE�Uj'e�gimsn��i��g�e�g�r�t�n�h{�1�% X

Page 24: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

"��imsmor�cÂe�¡i�ih{�k�ij��il e�g�mon��i�xg e�gir�tXn�hk��v�j�e�g�r�t�v�lÊvxtXh�e�n�m��ihkjot(gÊvxms��rXj��$ gir�c e�gir�xn��ke�vx��r[v�tXmonxjoj�e�g�rÀtXn�hk�8�ihklij'¡�rX�{nE� � r�moniu~e�girÀ��h{n~�ir[¡�rX��hkcij�e�n�tXn�ci���it�eXuie�gir�morX¡�|limsr��xrXc�e�hkci��mor���r�mojor-t(givxmo��hkci�]nx�,e�g�r�t�v�lÊvxtXh�e�n�m��'�'gir�t��imomsrXc�eÀhkc�eogir�t�n�h{�Å�ir�t�v�|~j� mon��i�xgi�k|���vxt�tXn�ms�ih{ci�-eogir#r�yIl8nxcirXc�e�h{vx�?�Õv�� r�yIl�rXt�eorX� nx�,v �, �tXhkmot��ihkeX��$n�}]nI��rX�Aeogih{j�ui��r�vxjojs�i}]r#eogÊv�eUe�g�r * "4� vxci���ih{n~�ir#vxmsr�hk�ir�v��K��h2�¿rx�`hkcijse�vxc��

e�vxcirXnx�ij+j��Uhke�t(g�h{ci�]e�h{}]rxuÊc�n�jor�moh{r�j+msrXjohkjse�vxcitXr�u8c�n���n���e(vx�xr���mon�l ��e�gir�| vxmor�h{�irXvx�j��Uhke�t(g�rXj(��� $ gir�c eogir�*E"4� hkj�e�msh{����r�mor��;u`��r�jsn��k�xr�e�girf}�v�e�msh�y�r �Â�Êv�eoh{n�c �� X��� n�m4e�girtXhkmot��ihkeÀ�I|Icivx}�hktXj]��vxj[��r��{�`v�j�jsn��k�~hkci��e�gir��ÂhkcirX}�v�e�hkt�r �Â�Êvze�h{nxc hkc ��* X����$ gir�c eogir#�ih{n~�ir#¡8r���h{c�jUeontXn�ci���it�eXu���r�r��{hk}�hkcÊv�e�r�e�gir�r<;8rXt�e�j�nx��eogir#t�vxlivxtXh�e�n�m¡�|]� n�mot�h{ci��� � % � e�n��xv�cih{jsg;� �4r�citXr�u��Ugir�c�e�gir[��h{n~�ir4hkj �sj��Uhkeot(girX��n�cAu ��eogir[cir��t�h{mot��ihke���|~cÊvx}]h{tÀr �Â�Êvze�h{nxcijU¡8r�tXn�}]r

��������

B � C = ��� �� � B I � C 8 � � �Z � ��� ) �� Z � � " � � � � � Z � � ��� � � a � ) � ) � �

� �������

�������� �������

���� �%� � � J �%� � � c ��� � �

� ��������������H

��������

��� �� � B I � C ) � ) �� Z � � " � � � � � Z � � ��� � 8#� a 8#� ) � ) � �

� �������

�������� �������

���� �J �c �

� ��������������=

��������B� &� C B� V C 8,? 576 , ��B� � C � ) � � ) � � ) � � ) � � ) � � ) � �

���������

�������� �������

T V � �%� �

T ��� �%� �

���� ��� �

� ��������������

� * ���

�'gir[�xn��ke�vx��r[n�c�eogir[t�v�lÊvxtXh�e�n�m�morX}�vxhkcij ��yIr�� ��v�e � r�monÂ��v�ci��e�girÀt�n�h{��tX��momor�c�e�ir�t�v�|~j+v�j4v-t�n�cijor��Â�irXcit�r�nx�$e�gir#�imshk�~h{c��-tXh{mstX�ih�eUmor�joh{j�e(vxc�tXrx�bdc jog�n�mseXu;¡�|R}]r�vxcij+nx��v�}�hkcin�m�}�n~�ih �Êt�v�eoh{n�c nx�`e�g�r�tXhkmotX��hke[r��Â�Êv�e�hkn�cij�uAe�gir*E"4� ��mohk�~hkci�-tXhkmotX��hkeUh{j'rXvxjs|�e�njohk}��i�Õvze�rx�

���!��� 1 N _ ' � ���#� � � ��� � � � � F � � ����� 3 $ ��rXmor�ui��r�jor�rÀe�gir�v-ed|Il�h{t�v��?jot(gir�}�v�eoh{tÀhkc �*h{���imsr-�����

% e

Page 25: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

Launchercoil

Vc

Moveable core

+

CR

Firing IGBT gate inputs

��h{����mor-�����`b ����� gÊvx����¡imsh{�i�xrÀ�imoh��Ihkci�-tXhkmot��ihkeX��+j+¡8r�� n�mor�u�eogir �Êmsh{ci��t�vxlivxtXh�e�n�m�h{j4t(gÊvxmo�xrX� eon�vxcRhkcihkeohÕvx�A�xn��ke�vx��r c 6 �:$ gir�ceogir �Êmsh{ci��l��i�{jsr[h{j�vxlili�kh{rX��e�n�e�g�r+e�movxcijohkjseon�m���vze�rXj�uitX��momor�c�e =ÊnE�Uj'�inE�Uc�e�gir[�kr�� e

�il�l8r�m�vxms} u�eogimonx�i��g�eogir�tXn�hk�$� e�g�r4�ihknI��r�hkc]eogir��{nE��r�m=�{r�� e�vxms} h{j=mor���r�mojor �d¡ih{vxjor��v�e-eogih{j�l8n�hkc�e���vxci� �inE�Uc e�gir�msh{��g�e�knq��rXm-b ����� vxci� ¡Êvxt � eon e�gir�tXvxlÊvxt�hke�nxmX���eÀjsn�}]r�jol�rXt�h��Êt-l�n�hkcÂe-���kh��xr#�Ugir�c�eogir�limsnzpsrXt�e�hk�{r�hkj+� �i�k�k|��Uhkeogih{c e�gir�t�n�h{�Õ��uw��rt(gin~n�jsrUeon�j��Uhkeot(g�n ;�e�gir�b �-���'jX�,�'gir�tXnxh{�it��imomsrXc�e�tXvxcicin�e=t(gÊvxci��rU��r�ms| �Â�ihkt �~��|�ujsn��Ugir�c�eogirb �-���'j��{n~n � �{h���r-n�l�rXc js�Uhkeot(girXj�u*eogir��knE��r�m��kr�� e�vxc����il�l8r�m�msh{��g�e�ihknI��rXj¡8r�tXn�}]r�� n�ms��vxms� ¡ih{vxjor��;� "���momor�c�e�hkj� nxmotXr��Z¡Êv�t � h{c�e�n�e�girftXvxlÊvxt�hke�nxmX��'gihkj�h{j�vR�irXjsh{m�v�¡i�{r�r<;8rXt�eXu=¡8r�t�vx�ijsr�e�gir�jsn�}]r�nx�Ue�gir�r�cirXms�x| hkc e�g�r�}�vx�xcir�eoh{t�Êr��{��h{jÀmsr�eo�imocir���eonfeogirt�vxlivxtXh�e�n�m[� n�m[eogircir�y~e�jog�nxe�� �+�kjoniu?jsh{cit�r-e�girtX��momor�c�ehkc�eogir�t�n�h{�:�sli��jogir�jÀvx��vxhkcijse �]eogir�msrX}�vxh{c�h{ci�-��nx�ke(v���r�hkc eogir�tXvxlÊvxt�hkeon�mXuÊe�g�r�tXnxh{�t��imomsrXc�e��ih{r�jÀn ; �Â�ihkt �xrXmÀeogÊvxc�mor��k|~h{ci��jsn��{r��k| n�cRe�g�r]t�n�h{� ��tXhkmot��ihke�mor�johkjse(v�citXr-� n�m�ir�t�v�|��

$ gir�c�e�girKb �����'j�v�morKjs�Uhkeot(girX��n�c�� �i�imohkci�Ue�gir��Êmoj�e�livxmse*nx��eogir��Êmohkci�4t�|~tX�{r���ueogir#tXh{mstX�ih�e'h{j'}]n~�irX�krX�fvxjUvxc �, -" tXhkmot��ihke'��joh{c��eogir#�ih{jstXmsr�e�r#t�h{mot��ihke�r �Â�Êv�eoh{n�cijhkc �� X���� $ girXc e�gir]b �����'j�v�mor]js�Uhkeot(girX� n ; h{c�e�gir]jor�tXn�c�� lÊvxm�e�n���e�g�r �Êmsh{ci�t�|It��{r�u;��r]vxmsr-jse�hk�{�*jon����Ihkci��e�g�r-j�vx}]r �! #" tXhkmotX��hke�� �4nE��r��xrXmXu$e�gir-t��imomsrXc�e�h{c�e�neogir-t�vxlivxtXh�e�n�m4h{j[msr���r�mojsrX�;�-�'gir-jsh{}]li�{r�jse[��v�| eon�}�n~�irX�$e�gir-msrXt(gÊv�mo��hkci��nx�=e�gir

% �

Page 26: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

tXvxlÊvxt�hke�nxm�hkj]eon mor���rXmsjor c � v�e�e�gir�e�hk}�r�jse�r�lZ�Ugir�mor ��rR�ir �Êcir eogirRjs�Uh�e�t(g��6n ;r���rXc�eX�)$ rftXnxcÂeoh{cÂ�ir�eon�eoh{}]rXj�e�rXl ��cÂeoh{��eogirftX�imsmor�cÂe]��n~rXj�eon � r�mon�vxci����nxm�e�girvxms}�vze��imsrÀr�yIhkeoj�e�gir#tXnxh{�2�

���!��� � � � 3 $ � � F � � � N � � � � F � � � � � � ��� � � ���hk���imsr � %�jsginE�Uj�v jst(girX}�v�eoh{t�nx�#v�joh{}]li�kr�jsh{ci�x�{r �2e�movxcijohkjseon�m�js�Uh�e�t(gZeon�l�n��{n���|�Ugihkt(g mor��{hkrXj#n�c vxc�r�y~e�r�mocÊv���mor�johkjse�nxm�eon �Â�ih{t �Â��|�msrX�i��tXr�t�n�h{�`t��imomsrXc�e�� � nxm�limsr ��xrXc�e�hkci�)��jo�it �¡Êvxt ����nxm���rX�knIt�hked|�msrX�i��t�e�hkn�cf¡�|fmorXjsh{�i�ivx�;tXnxh{�;t��imomsrXc�e�j����

Vc

Rq

Rc

+

Launchercoil

CFiringsignal

Moveable core

��hk���imsr-�^%I�`b ����� ���i}�l �°vxci� �'�Â�irXc�t(g �imshk�~h{ci�-t�h{mstX�ih�e���+j]¡�r�� n�msrxu�eogir�t�vxlÊv�tXhkeon�m-h{jt(gÊv�mo��r�� e�n jonx}�rf�ir�joh{msrX� �xv��{�ir�� �'gir�b �����

hkj[js�Uh�e�t(gir���n�c ¡�|Rvxt�eohk��v�e�hkci��eogir-��v�eor��imoh���r����'gir-�ihknI��r�h{j[msr��xrXmojsr �6¡ihÕvxjsrX�;uÅjsnt��imomsrXc�e =inq�Uj�e�gimsn��i��g e�gir]tXnxh{���Uhkci�ih{c���jX� ��e�jsn�}�rl�n�h{c�e�h{c�e�hk}�r�u?��r]�irXt�h{�ireonRjs�Uh�e�t(g n ; e�gir�b �-���À���'gir�t�n�h{�KtX��momor�c�e-�in~rXj�cin�e�t(gÊvxc���r�h{c�jse(v�cÂe�vxcir�n��ijo��|�ugir�citXr#e�g�r���h{n~�ir#¡8r�tXn�}]rXj'� n�m���vxms���d¡�hÕvxjsrX� vxci��tX�imsmorXc�e4¡8r���h{c�j�e�n>=ÊnE� e�gimsn��i��geogir��~��rXcit(gihkci��msrXjsh{jseon�m a � �K�'gir#tX��momor�c�e[�ir�t�v�|~j4}]n�mor+�Â�ihkt �Â�k|�e�givxc h��Å��r��ijor��jsn��{r��k|�v�� morXr��UgirXr��{hkci�-�ih{n~�ir��,�'gih{j'hkj�¡�rXt�v��ijor[eogirÀr<;8rXt�e�hk�xr#morXjsh{j�e(vxcit�rÀgÊvxj'¡�rXr�chkcitXmsr�vxjsrX��¡�|�e�gir��ijor�nx�wvxc�r�y~e�rXmscÊvx�ImorXjsh{j�e�n�m�� "�vxmsr�}��ij�e�¡�r�e�v �xr�c-cinxe$e�n[r�yItXrXr��eogir#}�vzyIhk}��i} c ��� nx�$e�gir#b ����� �Uh�e�g�e�gihkj'tXhkmotX��hke����e'e�g�rÀjse(v�mse'nx�$e�g�r �Êmohkci�-t�|~t��{rxuwv�j�h{c�eogirÀlimor��~h{n��ij�ed��n�imoh��~h{ci��eon�l8nx�{n���hkrXj�ueogir,�! #" tXh{mstX�ih�e`r �Â�Êvze�h{nxcijKvxmor'jsn��k�xrX�;� $ gir�c]eogirUb �-��� j��Uhke�t(g�rXjKn ;�u�g�nq��r��xrXm�u

% �

Page 27: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

��r�c�rXrX� e�n }�n~�ih�� |Ze�g�r�msrXjohkjse�vxcitXr�e�r�mo} hkc �� X���e�n mor =ÊrXt�e eogir limor�jorXc�tXr n��eogir�r�yIeom�v�jsrXmohkrXj[msrXjsh{jse�vxcit�r�limonE�~h{��rX�R¡�|�e�gir �Â�ir�cit(gihkci��mor�joh{j�e�n�m+vxj4��rX�k�,vxj�e�girmsrX}]nq��vx�Anx�*eogir#t�vxlivxtXh�e�n�m��D�4� e�r�m'b �-����js�Uh�e�t(g��6n ;*ui��r#gÊv���r

��������

B � C = ��� �� � B I � C 8 � � �Z � ��� ) �� Z�� � " � � � � � Z � � ��� � � � a!b7=�a � � � ) � ) � �

� �������

�������� �������

���� �%� � � J �%� � � c ��� � �

� ��������������H

��������

��� �� � B I � C ) � ) �� Z � � " � � � � � Z � � ��� � 8 � � a b7=�a � � 8 � ) � ) � �

���������

�������� �������

���� �J �c �

� ��������������=

��������B� � C B� V C 8!? 576 , ��B� � C � ) � � ) � � ) � � ) � � ) � � ) � �

� �������

�������� �������

T V � �%� �

T ��� ��� �

���� �%� �

� ��������������

� * ���

�'gir�t�vxlÊv�tXhkeon�mÀ��n���e(vx�xr�msrX}�vxh{cijÀeogir�jovx}]rR��vxj���r���n��i�k� r�yIl�rXt�e��Ugir�c e�girb ����� eo�imoc�j�n ;=�[vxci��e�gir]tXn�hk�,tX��momor�c�e��ir�t�v�|~j�msn��i��gi��| vxt�tXn�ms�ih{c���eon vfjohk}�l��{r�, �t�h{mot��ihkeX�

%

Page 28: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

� ������Q+��� V�� �

�'gihkj�v�lil8r�ci�ihÎy�limor�jor�cÂe-vfe�vx¡i�{rnx��h{}]l8nxmse(v�cÂe��Â�Êv�cÂeohkeoh{rXj#�ijsrX� hkc eogir�vxcÊvx��|Ijsh{j�ihkjot��ijojsrX� hkc�e�gihkj'lÊvxl�rXmX�� ���� ������������ �������! "��# !$����&%'�!��()�

* +-,!./,1032546#©�É�³q±°­2¥§¯RÓ�±s¯d­2²�«�Ìx²�­2±�³X­1¥¨©�Æ{µ 7 ³­1¤q¥¨¦ ÏA²�«2Ë�¸ ²�³qƧÐ98 ¯�²�½�Ì�²�³q±�³X­Èz¦�±oª�µ

: +;,<.=,1032)> ²�«=? 6#©�É�³q±°­2¥§¯A@zÈ B+ªE±�³z¦1¥Ç­ Ð

C D ,10E2F46#©�É�³q±°­2¥§¯ Ìx²�ƨ©�«2¥¨¦1©�­1¥§²�³ ªE±�³�¦�¥Ç­ ÐG ²�­2¤q±�«2Ï?¥¨¦�±�Ë�³q²(Ï?³+©�¦IH�½'©�É�³q±°­2¥§¦2©(Í­1¥§²�³�J�²�¬i©�½�©�­1±s«1¥¨©�Æ{µ

K 0L,M.�2F4ÄÅ«2½�©�­1Èq«2±#Ó�±�Ƨ²�¯�¥¿­ Ð G ¥§³f­2¤q¥¨¦4¯s©�¦1±�¸²�³qƧÐ�­2¤q±ON G ²�«�ÆDz�³qÉ�¥Ç­1È�ªE¥Ç³�©�Æ8¯�²�½�ÍÌ�²�³q±�³X­QPA¥¨¦?©�¦2¦1Èq½�±sª4³q²�³SRs±�«2²zµ

TVU D ,10E2F4 W ©(­2Èq«2©�­1¥§²�³ ½�©�É�³q±�­1¥¨¦1©�­1¥§²�³ ²�¬K­2¤q±¦�¤q±o©(­2¤4²�«Å©�«2½�©�­1Èq«2±�½�©�­1±s«1¥¨©�Æ{µXFY ªE¥§½�±s³z¦1¥Ç²�³qÆDZo¦1¦

Z?±�ƨ©(­2¥ÇÓ�± ½'©�É�³q±°­2¥§¯ Ì�±s«1½�±s©�Òq¥§Æǥǭ Ð²�¬A­1¤q±�©�«1½'©�­1Èq«2±�²�«K¦1¤q±s©�­1¤�½'©(­2±°Í«1¥¨©�Æ{µX U [�,<.=,!0E2F4 \ ©�¯°ÈzÈq½ Ì�±s«1½�±o©�Òq¥§Æǥǭ Ð ±oÖ�È�©�Æ�­1²]�^`_�¶oº 2)a ¥§³�6Eb W Èz³q¥¿­6¦�µc [A254d0E2F4 ÄÅ«2½�©�­1Èq«2± ²�«�¦1¤q±o©(­1¤ ±�Ƨ±s¯°­1«2¥§¯s©�Ư°²�³�ªEÈz¯d­2¥ÇÓ�¥Ç­ Ð�µe D f8²�¥§Æ~¯°Èz«1«2±�³X­+ + fA©�Ìz©�¯�¥¿­2²�«;Ó�²�Æ¿­6©�É�±N 0 ÄÅ«2½�©�­1Èq«2±,Ì�²X¦�¥Ç­1¥§²�³

g h ,1032)> W ­1«2±s¦2¦�­1±�³�¦�²�« G ¬ÎÈq³z¯°­1¥§²�³ ²�¬+½�©�É�ͳq±°­2¥§¯�¸�±�Ƨ±s¯°­1«2¥§¯8¾z±sƧªz¦Ê©�³zª�©�«2½'©(­2Èq«1±Ì�²X¦�¥Ç­1¥§²�³Âµi h ÄÅ«2½'©(­2Èq«1±�¬Î²�«2¯�±j k Ñ�¥Ç«2¥Ç³zÉ�¯s©�Ìz©�¯°¥Ç­2©�³z¯°±lnm [ f8²�¥§Æ�«1±o¦�¥¨¦�­2©�³�¯°±0po qsr ÄÅ«2½'©(­1Èz«1±,½'©�¦2¦� ªE¥§½�±s³z¦1¥Ç²�³qÆDZo¦1¦ t ÈE­ ÏA©�«2ªqÆÇÐÌx²�¥§³X­1¥§³qɳq²�«1½'©�Æ$Ó�±o¯dÍ­1²�«;²�¬�Èq³z¥¿­ÅƧ±�³qÉ�­1¤Âµu 0 ¼Â±�³zÉ�­1¤[²�¬�¯°²�¥ÇÆ~Ï?¥Ç³zªq¥Ç³qÉ�µv 0 £;¤q¥§¯6Ë�³q±o¦1¦A²�¬i¯�²�¥§Æ�Ï?¥Ç³zªq¥Ç³qÉ�µ

% *

Page 29: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

� ������Q+��� V�� �n�

��rXmor�u`��r���h���r�jsn�}]r�h{c�joh{�xgÂe�h{c�e�nReogir�vxmst�vxc�r �+}]rXmsh{t�v�c $ h{msr ��v��i��r�j�|Ij�e�r�} ��'gihkj�h{j��ijor�� �i�+� n�m�tXn�}]li��eoh{ci� eogir cÂ�i}�¡�rXm�n���eo�imoc�j�h{c v t�n�h{��¡ÊvxjsrX� n�c tXnxh{��ihk}�r�cijohkn�cij��

����� �3 ������ 365 � �

3 ������ � � �� � 3 ��� � 5�� ����� ��� 6'6'6�� � � � � 3 ��� � 5�� ����� ����� � �

� ����� ��� � �"!# � � �$� 3 �&% 3 � 365(' � ����� ��� � �)!� ��� 5 � � 3 �*� 3 � 5+,+,+,+ 6 � � � � ��- � 6 � 6 �/. 6 � � 6/0 � - 6 6 �+,+,+ 6 � � 6 . � 6 � � 6 - � 6 � 6 � - 6 � � 6 � 0 6 � � - � .+,+ 6 � � � - . � � � � . � 6 � 6/0�0 . 6 � � � � � � � - . 66 6 � � �/. - � � � � � � 6 � 6 . - 6 � � � � � � � � � � 6

6 � � - . 0 � � - � � 6 � � . 6 � � 6 � . � � .� 6 � � � 0 � � � � �

6 � 6 � � � 6 � � � � � � - . � 6 � � � . � � � - � � 0 � 6 � . 0 6 � � � � � ��- 0 �

� 6 � � 6 �

� � - . � � 6 � � � - � 6 � - � 6 - � � 6� 6 � - . � � � � 6 � � 6 � � 6 � 0 � � � - � 0� 6 � � � � � � - 6 � . � � � . � . � - 6 00 6 � � �

� � � � � � 6 � �/. - � � �

� 6 . � - . 6- 6 � � - �

� � � . 6 � � � - � � � 6 � 6 �/. � 0 � �. 6 � � � � � . 6 � 0 � 6 � 0 . � � � � . - 6 -�- � � . 6 6 � 6 . � � ��-�- � � 6 � .�. - . � � 0 �

. � � � �

6 � 6 . 6/0 � � 6 0 - � � � � � � - � 0 � � 6 � 6 - 6 - � � 6 � � � � ��-�- � � � 6 - � � � . � 6 � 6/0 � � - � -�- � � 6'6 � � � � . - �

� 0 � � � 6 � 6 � � � � � - � � � � � � - � � - � � � � . � 6 � 6 � 0 � � � 6 � � - � 6 � � �

� � � - � � 0 � 6 � 6 � 6 - � � . 6 � � � 6 � � 0 � � - � � � 0 0 6 � 6 � �

� � 6 � � � � 6 � � � � � 6 .�. � . � � . - 6 � 6 � 6 � 6 � � � � � - � � 6 � . � � - � � � . 6 � 6 � . 6 � . - � - � 6 � � � � � 6/0 � - � � -� 6 6 � 6 � 6 � - � - 6 � � � � . � � �� 6 � 6 � - � 6 � 0 � . � � - � � . - � . � �� � 6 � 6 � � � 6 � � � � � � � � � � � . . � 0 6 � . �� 6 � 6 � � � 6 � � 0 � 6 � � 6 � � � � � 0 - 6 - � � 0 6 � 0 � .� � 6 � 6 � 6 6 � � 6 � � � � � � 0 - � � . 0 �

� � 6 � � 0�0� � 6 � 6 0 . 6 � � � � � � � � 0 6 � � 0 � � � 0 6 � � � 0� � 6 � 6 � . 6 � � 6 - � � 6 � - � - � ��- � � � 6 � �

% (

Page 30: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

����� �3 ������ 365 � �

3 ������ � � �& � 3 ��� � 5(� � ��� ��� 6'6'6�� � � & � 3 ��� � 5(� � ��� ����� � �

� ��� � ��� � �"!# � � �*� 3 � % 3 � 365(' � ����� ��� � �"!� ��� 5 � � 3 �*� 3 � 5� 0 6 � 6 � � 6 � � 6 ��- � � � 0 ��- � - � � � 0 6 � � -�-� - 6 � 6 � � 6 � � 6'6 � � � � . � � � - 0 � � � 6 � � � �� . 6 � 6 6 � � - 0 6 � - � - � ��- � � 6 � � � � 6 � - � 6 6 � 6 6 � � � � 6 � � - � �/. � 6 � - � 6 � � � 6 � 6'6 - . 6 � � � � 6 � 6 � � � � � 0 � - 6 � 0 6 � � 6 � 6'6 - 6 � � 6 � � � � � - � � � - 6 � �

6 � 6 . 6 � 6'6/0 6 � - 6 � � 6 � � . � 0 - � � � 6 � � 6 � 6/0 �

� 6 � 6'6 � 6 � � 6'6 � � � 6 � . - � � � 0 � � 6 � 6 � 6 � �

� 6 � 6'6 � � 6 � � � � � � . 6/0 . � � 6 � � 0 6 � 6 � �

� 6 � 6'6 � 6 � � 0 � � � - � 6 6 � � 6 � 6 � 0 6 � 6'6 � � 6 � �

� � � 0 � 6 � 0 6 � 6 � - . - 6 � 6'6 � 6 � 6 � � � . � � � � 6 � 6 � 6 � � - . 6 � 6'6 � 6 � 6 -�- . - � - � 0 � - 6 � 6 � 6 0 �

� 6 6 � 6'6 6 � 6/0 - 0 � 6 �/. � � 6 6 � 6 . 6 � 6 0

� ������Q+��� V�� �n� �

�#vx�ijsj! ?r���rXci��mor#h{c�e�r���m�vze�h{nxc�nq�xrXm4v�e�moh{vxci���kr+e(v �xrXjUe�g�r#� nxmo}Y$Y�� � � 9 � � ] � ] � H �����

L � � � � � 9 � � � 9 � * ���Ugir�mor � � 9 � � vxmsr�eogir��{n~t�vze�h{nxcij*n��ie�gir�h{c�e�r���m�v�eoh{n�c�l8nxh{c�e�j�����h���rXc�h{c�eomoh{vxci���kr��knItXvx�t�nIn�ms�ih{civ�e�r�j(�Åvxci� L � vxmsr�v+jsr�e,n��Ê��r�h{��g�e�j*�ir�eorXms}�hkcirX��¡�| ?rX��r�ci�imor�l8n���|~cin�}]hÕvx�kj�ijsrX��e�nh{c�e�r�mol�n��Õvze�r+eogirÀ� �icit�eoh{n�c � � � 9 � ��nE��rXmUe�g�r#eomoh{vxci���krx��*vx¡i�kr %~� % � �#vx�ijsj � ?r���rXci��mor#��r�h{��g�e�j4vxci��h{c�eorX��mov�e�hkn�c�l8nxh{c�e�j'� n�m @ H ��u � He

hkci�ir�y � � � � L �� ) � *�� � * e � ) � ) (���� � %I� ) � ) � e ( � * % ) � ) (�� � � %I� ) � *�� � * e � ) � ) � e ( � * X ) � ) (�� � � %I� ) � ) (���� � %I� ) � ) � e ( � * e ) �k� ) *�� ) X ) ) � e e � ( e * � ) ������� � ( ) *� ) � e e � ( e * � ) ��� ) *I� ) X ) ) ������� � ( ) *� ) � e e � ( e * � ) � e e � ( e * � ) ������� � ( ) *

X )

Page 31: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

�*vx¡i�kr X�� % �<�#vx�ijsj �' År���rXc��imor+��rXhk��g�e�j�vxci��hkc�e�rX�xm�v�eoh{n�cl�n�h{c�e�j=� n�mA@ H � %Iu � H�hkci�ir�y � � � � L �� ) � � ) ��e`% � � ) � % e ( % * � ) � ) � * X ( X���e% ) � % e ( % * � ) � � ) � e`% � � ) � ) � * X ( X���eX ) � % e ( % * � ) � % e ( % * � ) � ) � * X ( X���ee ) � * X * % % ) ) � ) � X ) * ( ) � ) � ) % � e % % e �� ) � ) � X ) * ( ) � ) � * X * % % ) ) � ) % � e % % e �� ) � ) � X ) * ( ) � ) � ) � X ) * ( ) � ) � ) % � e % % e � ) � � X � � ) % � ) � ) � X�� e � ) � ) � ) ei��e % � � e* ) � � X � � ) % � ) � X�� ) X � % � ) � ) ei��e % � � e( ) � ) � XI��e � ) � ) � � X � � ) % � ) � ) ei��e % � � e� ) ) � ) � XI��e � ) � ) � X�� ) X � % � ) � ) ei��e % � � e��� ) � X�� ) X � % � ) � � X � � ) % � ) � ) ei��e % � � e�^% ) � X�� ) X � % � ) � ) � X�� e � ) � ) � ) ei��e % � � e

�*vx¡i�kr!ei� % �<�#vx�ijsj �' År���rXc��imor+��rXhk��g�e�j�vxci��hkc�e�rX�xm�v�eoh{n�cl�n�h{c�e�j=� n�mA@ H ��X�u � H hkci�ir�y � � � � L �� ) � X X X X X X X ) � X X X X X X X � ) � ) e * � ) %% ) � e ( X ) *I� ) � % � ) X e � ) ) � ) * * ) � XX ) � % � ) X e � ) ) � e ( X ) *�� ) � ) * * ) � Xe ) � % � ) X e � ) ) � % � ) X e � ) ) � ) * * ) � X� ) � * � ( X ( * ) � * � ( X ( * ) � ) % � � X � %� ) � ) � �I� X ) � ) ) � ) � �I� X ) � ) ) � ) % � � X � % ) � ) � �I� X ) � ) ) � ) � �I� X ) � ) ) � ) % � � X � %* ) � � X * e e e % ) � ) e * � ( ) X % ) � ) X * � � � * *( ) � � X * e e e % ) � X�� % * � � � ) � ) X * � � � * *� ) ) � ) e * � ( ) X % ) � � X * e e e`% ) � ) X * � � � * *�x� ) � ) e * � ( ) X % ) � X�� % * � � � ) � ) X * � � � * *� % ) � XI�^% * � � � ) � � X * e e e`% ) � ) X * � � � * *��X ) � XI�^% * � � � ) � ) e * � ( ) X % ) � ) X * � � � * *

X��

Page 32: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

�*vx¡i�kr �I� % �<�#vx�ijsj �' År���rXc��imor+��rXhk��g�e�j�vxci��hkc�e�rX�xm�v�eoh{n�cl�n�h{c�e�j=� n�mA@ H � ��u � H*h{c��ir�y � � � � L �� ) � X X X X X X X ) � X X X X X X X ) � ) %~��� * )% ) � ) *���e���e * % ) � e � ( % ( % � ) � ) e � e � * %X ) � e � ( % ( % � ) � ) *�� ei��e * % ) � ) e � e � * %e ) � e � ( % ( % � ) � e � ( % ( % � ) � ) e � e � * %� ) � * ( * ( ) � � ) � ) � ) � e % X ) � ) � � % % ( % �� ) � ) � ) �Me % X ) � * ( * ( ) � � ) � ) � � % % ( % � ) � ) � ) �Me % X ) � ) � ) � e % X ) � ) � � % % ( % �* ) � � � * * ����e ) �k�� ) � � ( X ) � ) �I� � ) * � (( ) ���� ) � � ( X ) � � � * * ����e ) � ) �I� � ) * � (� ) ) ���� ) � � ( X ) �k�� ) � � ( X ) � ) �I� � ) * � (��� ) � ) ) * X ( e ) � % * e ( % e ) � ) � X �����I� ��^% ) � ) ) * X ( e ) � % � X����^% * ) � ) � X �����I� �� X ) � % * e ( % e ) � ) ) * X ( e ) � ) � X �����I� ���e ) � % * e ( % e ) � % � X����^% * ) � ) � X �����I� ���� ) � % � XI���^% * ) � ) ) * X ( e ) � ) � X �����I� �� � ) � % � XI���^% * ) � % * e ( % e ) � ) � X �����I� �

X %

Page 33: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

�*vx¡i�kr ��� % �<�#vx�ijsj �' År���rXc��imor+��rXhk��g�e�j�vxci��hkc�e�rX�xm�v�eoh{n�cl�n�h{c�e�j=� n�mA@ H ��(�u � H(hkci�ir�y � � � � L �� ) � X X X X X X X ) � X X X X X X X ) � ) e * � � ( )% ) � ) % ) � X e ( � ) � e * ( � * % � ) � ) ��� � � X �X ) � e * ( � * % � ) � ) % ) � X e ( � ) � ) ��� � � X �e ) � e * ( � * % � ) � e * ( � * % � ) � ) ��� � � X �� ) �k�^% � * % ) * ) � e X ) * ( � ) � ) X * (I� X � ) � e X ) * ( � ) ���^% � * % ) * ) � ) X * (I� X ) � e X ) * ( � ) � e X ) * ( � ) � ) X * (I� X * ) � � % X � ( % ( ) ��� * * % ) X � ) � ) X ( * % X * ( ) �k� * * % ) X � ) � � % X � ( % ( ) � ) X ( * % X * � ) ) �k� * * % ) X � ) ��� * * % ) X � ) � ) X ( * % X * ��� ) � (�� ) � ei� ) ) � ) e e % ( �I� ) � ) �^% * * * e�^% ) � ) e e % ( �I� ) � (�� ) � ei� ) ) � ) �^% * * * e� X ) � ) e e % ( �I� ) � ) e e % ( �I� ) � ) �^% * * * e��e ) � ) X � * X * ei� ) � ei�x� ( * � ) � ) %I� � ei�� ��� ) � ) X � * X * ei� ) � % %I��( � X ) ) � ) %I� � ei�� � � ) � e���� ( * � ) � ) X � * X * ei� ) � ) %I� � ei�� �� ) � e���� ( * � ) � % %I��( � X ) ) � ) %I� � ei�� � * ) � % %~� ( � X ) ) � ) X � * X * ei� ) � ) %I� � ei�� � ( ) � % %~� ( � X ) ) � ei�x� ( * � ) � ) %I� � ei��

X X

Page 34: Notes on FEA modeling of Coilgun Mass Accelerator Bill Slade

� Q��xQÀ_`Q+� S�Q�BÎ�DC �-�G$ �4*I�{vx�ir�u ��� jsh{}]li�{rf�ic�h��Êr�� lig�|~joh{tXvx��}�n~�irX�'� n�m�v msrX�{��t�e(v�citXr vxt �t�rX�krXm�vze�n�m�u ���������� ! �� ��� �� ���{u,��n��1� ei�xu,cini������u`lil;�-e`% ) �'e`% ��u @�nq���% ) ) �I�B % C �$� �$�7*Ihk�k�xrXjseorXmÀv�ci���#� ���A�ÊrXmsm�vxmsh2u�� ��� ��� ��� # ��� � �������� !�� # ���� ! � ��# � �!� ��"��� ��!#�u "�vx}�¡imohk�i��r ��cihk�xrXmojshked| �`mor�joj�u$��( ( ���

B X C�$�� �*�3��� ��vxj�e�n�j�vxci�$@�� *�vx��nq�Uj �Âh2u�� # ���� !��%� �� ����� � �&�'� ( ��#����!�*) +-, � ��� ���# ��� � ����� ����.�� (%�u . vxmstXr�� �[r��`�xrXm �`�i¡i�kh{jog�rXmoj�u % ) ) XI�B e C ��� . � . vxt(gÊvx�in�u ���UyIh{js|~}]}�r�e�msh{tUrX�i�I|�t��imomsrXc�e�l�mon�¡i�krX}]j=�ijohkci��v�jol�rXtXh{vx�g�|~¡imsh{��� E � � E }�r�e�gin~�;u �/�������0� ! �� �1���� ���{u~��n��1�EX (Iu�cini� X�u�l�l;�A��� e XM��x��e ��u . vE| % ) ) X��B � C �$�#*8�A*�v�ci��gÊvfvxci� ��� �Un~�i��rXm�u � �[rXjsh{��c�v�ci� vxcÊvx��|Ijsh{j[n����xn��ke�vx��r�� r�� vzy`�hkjs|~}]}�r�e�mohktvxt�eo�Êv�eon�moj�u �2�#�����3� ! �� �4���� ���{uÅ��n��1�AX ) u$cini� �Iu$lil;�#X %Me ) �X % e X�uC*~rXl�eX�$��( ( ei�

B�� C "+�3�+�A��vqpovxciv�e�gÊv�c vxc�� �-� �4�;u �8E`�{r�t�eomon�}�vxt(gÊvxc�h{t�v��,�*movxcijsh{rXc�e "�gÊvxmovxt �eorXmsh{jseoh{t�jKn��?vxc]bdci�i�it�e(vxhkn�c �+t�e��Êv�eon�m=¡�|]��h{cih�e�r E`�{r�}�r�c�eG�+cÊvx��|~joh{j�u �5�������� ! �� �6���� ���{uI��n��1� % ) uicin��C%IuÊlil;� % ) ) ��� % ) ) �Iu . vxm��?� ( ( XI�B C.$ � ��� �`mor�joj�u *�� ���x�*r��E�xn��kj��Âh2u $ � ��� �=r�eoeorXmo�kh{ci�[vxci� �+� �$�����{vxcicir�ms|�u!7 !"� ��! � ��#�8 �� �:9 �� ���<;>=?=A@B��. �DC !E���F�AG�� � � ��� � , �5;��%�H9 !� ���!�xu "�v�}�¡imohk�i��r��cihk�xrXmsjohked| �`msrXjoj�u % ) ) %I�

X e