From ccf492d7263a5176c65eee59dcf2fe1951b2d878 Mon Sep 17 00:00:00 2001 From: Janita Willumsen Date: Tue, 24 Oct 2023 22:36:04 +0200 Subject: [PATCH] Final, for real, changes --- latex/main.pdf | Bin 746541 -> 746691 bytes latex/sections/results.tex | 6 +++--- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/latex/main.pdf b/latex/main.pdf index 03e7eef8a9bb2336bdd5fa1b010830b4098e1123..59829820a78c34dc8d8da63020d9749cff3dbcf6 100644 GIT binary patch delta 3606 zcmajhXEYlCzXtG-5JIg`6t!Zn2x>I;-lO&m6(m))t5#wZtu01XH9}RXy+>Puma5g3 zidB2GRBN<$y}kFG_niCfe)yg9|L}Z#&U5}XgED>ZW$=kq&D8g91LYM}3A@?ixJf6c z%$0Ynu|y9t@;o^T`@Vm9-=*k<~XLACxi2gJ34vkxwKWB)=V3-C* zz#BA@<-@#I7~2xI9YWQj2{g_lW}u&-@`U^T`lYFy8~EGDi568A*-F_; zm8^{yG;>m0`xoZpYiQ5hldw=XmW1mCy{?7dOcUS-KV{SIMX!GWB1ewg$~V-b?R>wg z9V|+bAX|ERVXtLyMeFxyr|?zuaS%z8nGnAKs-XteGD49;E5Ku{9la&RFGuyN) zYW|>FHc8X3%HFHZIQ#(fhM*x8QJE)e1kEK0!S*?7DBqWe&KK&_TQnWr+<@wbB zCsf7L{L)0R>DesJw|t@szn+x$@jYi@Jjaqy9+cldG2+H+jpSO4?Ov}*EMG3LM&edf z4GG33O6tPC{3_cXUre>z*Dxddy##_um?h`q*y)N}=QQl0Y;lx9#NQ&A(DdM{V@fBu zs2|jHwfd3e-Iy`On^1Puh(YxXO`?iE`(-x3wKqNy@sh8$oKC!!L3ZLnr}Pe(@g9hn zJnnFe__5Q3Q&;&3FtsBSJ6%&sohQfJ9-mD+Z3yiJC1DZPWG+?ZCpx!GW2j2#$kMoB zYVl3=CB?-pkdW)8hE&TS!R<}$+!2}0St3v9$dRE`?s*VTw$0AN#(44aPTlB_;QdiHyT{~IFsfIg1|0qGUzVh*nj?!C^;zU zI_w|mQb#(*ENsufQ$~4w<)#6nJvch2pb@&1mj-|o<(f#Js zf#x{s?(kl_EB>H#rk|O5-2kv-%S2t-=^AY`%ZgkAY2YU0!q5VgMXEW?%TCXcujRnE zBCONV-xGTmvc(RZ-BBW_0Mv{}Sb^DJY)u6!L9sSQ}!!3NU~K;(QF@%Y=Y< z@*e852VBd6;G6`qz=k#DSZTAUB^olws9)N2jl5DKwK6x*Wyq3dzn4@YnAWj|nG3L7 zGn~Eg7qg8q`r!?j_^|&Be>O`rY^&2XJbN>4tsXjvVmLZORtO@ssiWvEhc3tCAjk(+ z8Lu`Zaz{JvVj)4ZqV=DM$2 z)p(0CPIliHTgRcn3=%%m8p{|8uB7*jRh>U0VZWEDT>B4u=EoOx>m80Gz)|_YaQVOt zk74*a1IdH1H{1u)zx^Ty5BZ=wkG#RZ(u*~Yp}T+tj~bh9KNE43D+pS_n=OrnA;OeM zV1{XykHBof7r234fft6r>U)2iY28t1bDo@%2L5`wD&DsM*%Xe0RL{-+$p_lQ?09lk zL|_h$1>bjbz8j1w#-oVTAGQ3t^;@3Rn&B*+Jtg+50l?0>{5#^K%x|?N z_RukYnWwTn;G{%jN3kb8W-pqI3O_~1rBqbNlzH9U5%AL2I^Z7YxE$5*DIpnbbj;ZF zIzzX3i;~XZ4ilsNzP2f`E~UbnI=f<$%b@n8KT!OFtGG_m=ALOE6>qt`z!w3qBi(kN z8LU9Gat4?5ISvgiLq6dWvu&paz3I^U@F#cRMx6cfmQLr>vLDeSfmd1jl8UjaM`0lp z>&&X#pP*x$3kp!u-$&Rqd86d;BQ4KIkhJ(uc7Dpa=h{Ep=MzF+aJn6j_gA7Gdc4&F zEIkk$iX>Nq-pHO6?=xiG@XCgu1H3~*gVCP1A?Rd$81+BEe?b4x{6qT>_#e7|=-cpN zknVL+B{*CPju3;x#Uvnd=6AgHJVVg};(BTbI6^@lj!;A(6#hlp(5?*b)HeDGItI#c zMV)J^+6v0L2qkTue+fN#Jp*|q107XGB@F@O{~K|G$eE!7d_(;NLu*t^pbh{QXY=}`vRR0t@KHDFZwSIz4w>SHb&<<4$p9ht{YEWOjUOcm$-N> zRSSZI{yr^Z6K8d3naYSo5MrFlZduKv5jbfDY^i6xrp-6e z=QA43CF*po=W@QHm|4Alq9_G2Tf*I{%h0UDvyBg@fQy$6ZvAk^b)v*VL)JB_gtp`7 z$NS<0xe}=~W`R*oGslr6%Q>j7#ayaP_`1_3r}9Nl{>CD*Tg6=Il0rRk?And=9)M}r z{XP^9!-**h2KaxdHV?N8|J-L=Y+Dw1*}tnsuGP?x{CDoL-@FPh zAIrvOQHuvIm`pOx|41SDR8r8plMD_Fkv$19VRr$=l(^qTr=_MzHgj*HpH!a8Y&;;J!J z6!sdx^wT*}(MwE7SCw}}9OQj^}?aLFiKrT@c5m!WluvE;@L6aPGl zWP_br?T?&*voYh7-8;g}-63hMj0<22;7B-w}pC6iTbNJJ_t%sgWBdTDjRI zkj49^93?&w+jFodT?8d>^P9XttBLyoGK*7W+Qct+LgKRy{gWKtwPU+?={azbKoh#W zUs6TYNC_;iOAYMb$i{*m%fpLLTX~USI-D@4Gm3G}R{8|eM`rqxgz?3^?*~~5J(BW< zu8Y#xWQ##PI|gxuXaHfo1pvahg1b6lQbAuG`niC5e@r1eT0~Kc1Kxq0{`LF6bx_n1 zQ`83g-w&tIUjJ_i;L6dNFg_gr^!W~zXpZmMsRjjn-Xs1Cn8WxQ$a(@s~gh>-3Pk|uMsL#7thvQ8JDg>I|MBIussi<$g`Q8=Irj%T|Z^V5`P=}&xf zfoCPma-jj5YrOZJ$NqNKYB;$n*mx(}$4)!PW6$2sNHl7y%H(}B?aL~df|{pYi+6tY z3dsQR^U%dks<1A$9$V&Z-}NLH>BQ&ccCkSFe*J0-Hq|@zuo|1YJtu6hWc=rMmqqaX zyTZx~tz*ux!%<6nT#Lz0D*ELN>~OZiVy}rf+o-$8pFw!@dwn~NyRfzD`p&qNJ;&Px z$BQ<%Wd{qV7MC;SHT&Nw7w7jQ;-lJxaq9dXn$Y9JwZT3);ai6{e}10N&e_U7GkLa6 zFgoVX9>NK=$l4U7D%$Ej{w_2kCR}q?dR}8RHI=>W>^*jv%^bt8M@vj)B&Mdlx~v-c zxuEAJgS7UQ3%`$@T_#!fH*7lL+?p-MjcVh#*?|5M$A)%hZp%KAoABeJ| P5(2Ia5fRb1G=TgEKaZra delta 3392 zcmV-G4Zrfk$t|tOEr5gpv;ui;128Z$lkt%#f7Mu9kL$J(e&1iAzG;D&A;o)xAm}Y= z3KTd+7d;P6188k}S2?!qBg@@vetl;+q%3*0u}?NFQ22r5XiN@=-+VJ9FCGeBd~@^r zyPMCyu2kWfH}9wic$vkE3qd?hpMSe`#UFP!e}iBCw1DXrqxqthQWg%ZG%8vN>q*6g z(q!P*-+sex7nK#IgH}mdzPqhlS$BQ2+ywg4clGT;+wzC7?04NW3F{u)s;p`F(ER(h z@?~gAx`)PF9T?a3yyD=;C1W?I-^fC)c~iP3zsnDCl$FQ<@jf2EH; z(=Q<5<{;q`BpgA)O(EgVyfzOB?QK5spJpJTn6YXM2`>gnxEV+QP|^|npCdvF%eX+Q zFu*Z7!$JyY5-f)9E3gp!1upWWi_xqv!7(f?H8WmJAfikO+W{|D*^40A?hq|>^xHrl zr!UbZ(B^F)XxOyW*3`Ts(6r=Se-HrH_Gyv#kD&`Q*x{37-X{$(nt5wYf)3F1f-?^g zi&|m^U>4%b7bB&*UClxjpf!-!b<0)PEZ2Zbq^lyRcgG$F@*K5*du4t3{fu2+GNaU| z+4YJW+_@JP%FHhsouU8d&RC={w;teWrg4?SdmL3~**f;%Uz$U%%&2bKe|ocdzJ+DL z$+FVrJwo{z`?5S7?}746`NOR!0qUZJMOx@T;Ach55cQr9eb`dJ-%(qqVY3a3RiNY; z+7(6za4GF1TO^p$$pha(;DyZ!Pn=7jp${=8r1NPt=yYKZtVMxl%btWy;#ciQI~K|? zr-zLC)mNl5@d`N6Rbs@jf4J@w8i~t!4zzb%J)fDd24LpXfEoxXda?`RM8#bs0BrZ* zwi5@SWE0js_3G5F8rZ#ra8Ev>kK6sG0TbYFWV{_4?_q;xK;n94e}Kv1J5Y)-u6&Qj z9dLSEF6)-|QSpj7V8qEj4gohTc=;F^?uiEE2I#yn7=BLzN|Vnt3lu2+4s%ev>pzVIZ8P zLk+_!j(L?S(2H9Cn1_;7t{7>}qf#&{#br>APEA=moEmx}V-mXSE)2Zj7(WBz$75)h zO*{%|W7@%%4iGwBf89QW8IM41WV!f79+7-PITot!ky16YSr07c^IG3=&H0Q)4gz_= z@o#5lshEWe0G}>1oHfY$2AUFT@&p#o%N|#DElmTPz)3NN< z=>U~y4pPD71o@i{;T4u@GF!npB{viy+fu&*P{d*uqyP$ve31Lf2fp`9S%b4^+I_kCqNp0dHZR#x_Jkiqz6$=^v9uRA{N)9}kZ)gQ?7$ zQ98;5$by*Zl@OFHk|L3^W7dhOL*vaP7mE^ZuT(6ee#)m>GGS9;IB>m&=EwbJ*Tq3f z-Y9*I0|W;Wf3npj5~wbc02puFB@)0Lay4dw*Fa+~9hkiYn(7j0>?P1tSKE+5qhtJ$ z>z9xKLr484rC(tn2XXPT7eDJ43FT4@eXR3#_h3VYtgH+bY`T2t z>eaE{kSt|tR9{m&f-WkocOA*=ZOTHBOO=w-eWZe5f5w?oF|OTt{US#gQvgCY!I+rY zD-ciR#~AyPwmSy_0VRMn`u)vC!%fF8Fz`W3!B zbfNC?)T3JVmeByWSG={TG>3$-+2EZJ%ihCr(~~rEu;z4s^d*q>15S;idwPaCMp}n& z@r3XLfAO_Gu@8O6yQ?k9;>BF`wN2#~md235=wc+yl*BB#0Og@RG;pJcLZrWt^nvBD z{`9K+L+JXN7!mQCjp{2U|3B8(Xe{29nx&#cK$5BIm4Z~f6zq~|X?FU8e z?+!%uc~g3O{h2WkEXMdh9@QHM|D?Oc_9VWp88Oe#a=L8Qa!Cg@pit5)* z3G%;IM_iv0R4xo9-S^=L>&;=8uVE%W0#A_e65a40qF(5n;0*(MH9+Zzs8PO7D{WsV ze`8$ROL>Wn?Gdpvj_!%rGBiZp5LIMOhv4y2Pv z+hBZ#Rb*>@y7|N3D8fL2N@MD!uy_%ypWct#zQ-?PxeT9h=?)X0B-N zyxg;qZn93gyr0=JydL3WY~7{@9UPoHUn0ISYAg~}8InFiG4|s2=>@p%CvU-+z#zk< z=NBBOE6kZ8<6Ux1 zMMFLyJVr4xK`=EzF-0>&I5jjgLqRz-I72c3KVDyw3JfbZGk>`R1;B2-2C03 z2^(}}A}e%ZB5|Y1S(&KO1<{=g6E(VEWejmcRiZ|NCQa)9d%F4L{O3;Z++k}##6%3dm)f1>P` zvU$q$q3pR5TP3ziY?Y2{r=*)-bdrAIU}SyFF&^xucT4Kls@)r1Q<|u&9JSAgva;t& zM0Emq&Xs^DBSQ(Cl4m7rx*tfG9)wZgVOOH3$AH)>dC~JgUX)}jp;1z&ObaD&N^+Fv zR~a`-!j!-%AymSzY_jsCsO{=Jf3V3)K$JaK0-|I?iG`8~U6N$E$w`uZKT`dpwPXNN zlK$&~EqkCBc(8o|`q{FxRB2$O`2-kqJ_97e7Xg#dGhRKD)iXss6VvB``RAEPz7iUt z3Yc7;Z1}BE1GP{G^{@q+p&PbA7i@=4Xn~#33Ok?;+MxrO8-7rdt}S-Ie?!1T@{E7K z2lm1+Fbe#LB%@+qW~%rDz%22M5zhqihk?24c};i*yuSdGlFUA`znuccgP#T_gP(y@ zbk|PGyT_k~GeE}!NBucq2>OdK#{s+Wd02o;a2c+^A}ql&tiV;c2G`*Rko({yKUvB} z27wf?(}7J6>~COegS|BEe|>2q++L9OGR#Zz%62NG98FRi$Lw9$QrciG)KyoB9+faYHmg9*`tQnBh7asEuTl)_>0bT zq-P{jcsVjO9@$$H3>kS68GRTzvL2cE-IrEm3oIBGe`wjdyGD@KQj%Z%EPl4~ockZ| W6&v7}nq&(f3NSV>3MC~)Peuw%)LgUx diff --git a/latex/sections/results.tex b/latex/sections/results.tex index c724d01..8960f00 100644 --- a/latex/sections/results.tex +++ b/latex/sections/results.tex @@ -96,10 +96,10 @@ In figure \ref{fig:two_particles_radial_interaction} we see the movement in radi \label{fig:3d_particles} \end{figure} -Finally, by subjecting the system to a time-dependent field, making the replacement in \ref{eq:pertubation}, we study the fraction of particles left at different amplitudes $f$. We can see how the different amplitudes lead to loss of particles, at different angular frequencies $\omega_{V}$ in \ref{fig:wide_sweep}. We study frequencies in the range $\omega_{V} \in (0.2, 2.5)$ MHz, with steps of $0.02$ MHz, and find that angular frequencies in the range $(1.0, 1.7)$ is effective in pushing the particles out of the Penning trap. +Finally, by subjecting the system to a time-dependent field, making the replacement in \ref{eq:pertubation}, we study the fraction of particles left at different amplitudes $f$. We can see how the different amplitudes lead to loss of particles, at different angular frequencies $\omega_{V}$ in \ref{fig:wide_sweep}. We study frequencies in the range $\omega_{V} \in (0.2, 2.5)$ MHz, with steps of $0.02$ MHz, and find that angular frequencies in the range $(1.0, 2.5)$ is effective in pushing the particles out of the Penning trap. + +We explore the range $\omega_{V} \in (1.0, 1.7)$ MHz closer in figure \ref{fig:narrow_sweep}, and observe a loss of particles for amplitude $f_{1} = 0.1$ in the range $\omega_{V} \in (1.3, 1.5)$, for $f_{2} = 0.4$ in the range $\omega_{V} \in (1.2, 1.6)$, and $f_{3} = 0.7$ in the entire range explored. When we introduce particle interaction, we observe the amplitude with higher value will result in a larger bound for the particle movement, and particles are easily pushed out. When we add particle interaction the angular frequencies, which result in particles being pushed out, are similar as in no interaction. As we see in figure \ref{fig:narrow_sweep_interactions} the particle's behavior, when interactions are added, is disrupted and add to the force resulting in the particle being pushed out of the Penning trap. We see that fewer particles tend to be left in the Penning trap, than without any particle interactions. We also see that the fraction of particles left is more unpredictable with particle interactions. -We explore the range $\omega_{V} \in (1.0, 1.7)$ MHz closer in figure \ref{fig:narrow_sweep}, and observe a gradual loss of particles for amplitude $f_{1} = 0.1$. Since they are additive, a greater amplitude will result in a larger bound for the particle movement, and particles are easily pushed out. Certain angular frequencies are more effective in pushing particles out of the Penning trap, when we add particle interaction. As we see in figure \ref{fig:narrow_sweep_interactions} where $\omega_{V} \in (1.3, 1.4)$ is also effective for pushing out particles of amplitude $f_{1} = 0.1$. When particle interactions are added, we see that there tends to be fewer particles left in the Penning trap than without any interactions. We also see that the amount of particles left is more unpredictable when there are particle interactions. -%The particles' behavior, when interactions are added, is disrupted and add to the force which result in the particle being pushed out of the Penning trap. \begin{figure}[H] \centering \includegraphics[width=\linewidth]{images/particles_left_wide_sweep.pdf}