text:
\section{}
\section{Introduction}

When the supersonic solar wind flows past the Moon, it leaves a cavity behind the Moon known as lunar plasma wake. Recent observations in the near-lunar wake region (100 km to 200 km from the surface) have revealed the presence of protons \citep{Nishino09a,Nishino09b,Futaana10b,Wang10,Wiehle11,Dhanya13,Halekas14b}.  These protons, which are basically solar wind protons, reach the near-lunar wake due to various processes \citep{Halekas15a, Bhardwaj15}.

Protons were found to enter the lunar wake parallel to the direction of interplanetary magnetic field (IMF) at 100 km from the lunar surface by SARA/Chandrayaan-1 \citep{Futaana10b}. These observations were at solar zenith angle (SZA) of $\sim$140{$^\circ$}\ (50{$^\circ$}\ behind the terminator) and the IMF was dominantly perpendicular to solar wind velocity. The energy of the protons was higher compared to that of solar wind and the density was around 0.1\% of the solar wind proton density.  The simple 1-D model for the plasma expansion into the vacuum \citep{Gurevich73,Samir83} did not explain the presence of these protons. In the mid-wake region of $\sim$3.5 R$_L$ downstream (R$_L$ refers to radius of the Moon), ARTEMIS has also observed protons parallel to IMF \citep{Wiehle11, Halekas11b}. These observations were found to be in agreement with the 1-D plasma expansion model at this distance. Recently, \cite{Halekas14b} have investigated the one-dimensional solutions for parallel filling of the wake using hot ion distributions (rather than the conventional cold ion approximation) and using Maxwellian as well as kappa distribution functions for the solar wind electrons. The solutions were compared with ARTEMIS observations and found to be in agreement.

Several observations have also shown that the  protons enter the near-wake in a direction perpendicular to the IMF. \cite{Nishino09a} have reported observations at 100 km altitude and SZA closer to 150{$^\circ$}. These protons from the solar wind enter into the near-lunar wake due to an increase in their gyro-radii under the influence of the electric field at the wake boundary. \cite{Nishino09b} have reported protons at 100 km  altitude closer to SZA of 168{$^\circ$}. These protons had a wider energy range: starting from lower than that of solar wind to well above the solar wind energy. The maximum energy observed was around six times that of solar wind. Backtracing of these protons showed that they are solar wind protons scattered at larger angles upon interaction with the dayside lunar surface  \citep{Saito08, Holmstrom10}. Their trajectories under the influence of the IMF and the convective electric field of the solar wind ($E_c$) provide access to the deeper lunar wake. \cite{Wang10} have reported protons in the near-lunar wake closer to the terminator regions of Moon. Closer to the terminator, these protons had energies less than that of solar wind, whereas their energy was found to increase further inside  the lunar wake.  These protons, which travel dominantly perpendicular to IMF, were proposed to be the solar wind protons that are forward scattered from the lunar surface closer to the terminator region.

In all the above  reported events the background IMF was dominantly perpendicular to the  solar wind velocity (flow).  Later, \cite{Nishino13} showed that the mechanism by which the surface scattered protons reaches the wake \citep{Nishino09b}  operates for other IMF orientations also, except perfectly aligned flow, where the convective electric field, $E_c \sim 0$. \cite{Dhanya13} have reported the proton observation in the low-altitude (100 km) wake  when the IMF was aligned with the solar wind flow, a case where parallel entry along IMF as well as perpendicular entry under the influence of convective electric field cannot play a role.  The energy of the observed protons were higher than that of average solar wind energy by few 100 eV. Those protons are from the higher energy tail of the solar wind velocity distribution. They access the deeper wake due to their larger gyro-radius.

In the context of entry of the protons to the near-lunar wake by various mechanisms, we have investigated the characteristics of velocity distribution of the protons in the low-altitude (100 km to 200 km from the surface) wake by using all the available data from the Solar Wind Monitor (SWIM) sensor of the SARA (Sub-keV Atom Reflecting Analyser) experiment on Chandrayaan-1. This will help us to understand the different proton populations in the lunar wake.

\section{Instrumentation and Data Sources}

 The solar Wind Monitor (SWIM) was one of the two sensors of the SARA experiment on Chandrayaan-1 mission \citep{Bhardwaj05, Barabash09},  which was a polar orbiting satellite around the Moon. SWIM was an ion-mass analyser with a fan-shaped field of view (FoV). The SWIM FoV was divided into 16 angular pixels of resolution  $\sim 3.5${$^\circ$}\ (elevation)$\times 10${$^\circ$}\ (azimuth), depending on the viewing direction. The energy coverage of SWIM was 100--3000 eV/q with $\triangle$E/E $\sim$7\%. SWIM measured ion flux in logarithmically separated 16 energy steps. The measurement for one energy and direction takes 31.25 ms. The SWIM FoV plane was almost perpendicular to the velocity vector of the spacecraft. One edge of the fan-shaped FoV looks toward the Moon and the other to the zenith. Assisted by the nadir-pointing spacecraft motion, the FoV covers $\sim2\pi$ (half hemisphere) within half of the orbit. However, this means that the SWIM FoV plane changes its orientation according to the latitude. The FoV plane is in the ecliptic plane closer to the equator and it was perpendicular to the ecliptic plane closer to the poles (more details about FoV orientation can be found in Futaana et al., 2010 and Dhanya et al., 2013).

	Due to the motion of Earth around the Sun, the orbital plane of Chandrayaan~-1 had a drift of
	 $\sim$1{$^\circ$}\ per day with respect to the Sun. This helps to have SWIM observations closer to
	  the dawn-dusk terminator (March--April 2009) as well as in the noon-midnight plane (June--July 2009).  Chandrayaan-1 was in a 100 km circular orbit till mid May 2009; subsequently, the
	   orbit was raised to 200 km. The SWIM data obtained from both altitudes (January--July
	    2009 period) are considered for the analysis in this paper.  After excluding the days when
	     the Moon was in the Earth's magnetosheath and magnetotail, about 500 orbits of
	      observation data in total is used in the analysis.

For the upstream solar wind parameters, such as solar wind velocity, density, and IMF orientation, we have used level-2 data from the SWEPAM and MAG instruments on the ACE satellite. Since ACE makes measurements near the L1 point, the data have been time-shifted to the location of Moon by considering the solar wind speed and distance of ACE from the Moon at each instant.

\section{Co-ordinate systems}

For the analysis, we have used mainly two co-ordinate systems:\\
 (1) aberrated Lunar-centric Solar Ecliptic (aLSE) co-ordinate system, and\\
 (2) Lunar Solar wind Electric field  (LSwE) co-ordinates. \\

 In aLSE co-ordinate system, the $x$-axis is towards the anti-solar wind velocity ($-V_{sw}$) which has been corrected for aberration due to the motion of Earth-Moon system, the $z$-axis is towards ecliptic north and $y$-axis completes the right handed co-ordinate system.

  In LSwE co-ordinates (see Fig.~\ref{fig:lsweframe}), the $x$-axis is towards the anti-solar wind velocity (similar to aLSE), whereas the $z$-axis is along the convective electric field of the solar wind ($E_c =-V_{sw} \times B_{IMF}$), and the $y$-axis completes the right handed co-ordinate system. In this co-ordinates, IMF ($B_{IMF}$) will be confined in the $x$-$y$ plane with the $y$-component always positive. The processes by which the protons enter the near lunar wake may depend on the orientation of IMF and the convective electric field, whose direction varies. The LSwE co-ordinate system helps to confine the direction of IMF in specific plane and that of the convective electric field in particular direction.

   \begin{figure}
       		   		            \centering
       		   		            \includegraphics[width=30pc]{fig1}
       		   		          \caption{Illustration of LSwE co-ordinate system. The $x$-axis is along anti-solar wind velocity, $z$-axis is along the convective electric field of the solar wind (${E_c} =-{V_{sw}} \times {B_{IMF}}$) and the $y$-axis completes the right handed co-ordinate system.  In this co-ordinate system  IMF (${B_{IMF}}$) will be confined in the $x$-$y$ plane with the $y$-component always positive (sample direction as red dotted arrow).}
       		   		     	   		\label{fig:lsweframe}
       		   	    \end{figure}

   In addition, we have used the solar wind rest frame, which is a frame moving with the solar wind and hence the convective electric field is zero. This frame has been used to discuss the velocity distribution function of protons in the wake where proton velocities are resolved into components having direction parallel and perpendicular to the IMF.

\section{Observation}

	SWIM made observations in the lunar wake in every orbit, initially  from 100 km altitude, and later from 200 km altitude. The location of the observations in the lunar wake in LSwE (spacecraft location) are binned into grid cells of size 100 km $\times$ 100 km.  The differential flux observed by SWIM when the spacecraft was located over any grid cell is accumulated in that grid cell.  Since there will be multiple observations over any grid cell, due to repeated orbits, the accumulated counts on a given grid cell is divided by the number of observations in that grid cell to get the average differential flux. The 2D maps of the number of observations in the lunar wake and the observed differential flux, projected in   different planes of the LSwE co-ordinates are shown in Fig.~\ref{fig:maplsew}.

	The top panels (Fig.~\ref{fig:maplsew}a to Fig.~\ref{fig:maplsew}e) show the 2-D map of number of observations projected onto  different planes. In most cases, there are several observations over a given location. The corresponding differential flux  has an asymmetry  along the $-z$-axis ($E_c$), with higher differential flux at the $+E_c$ ($+z$) hemisphere compared to the $-E_c$ ($-z$) hemisphere within few 100 kms from the terminator (strip in red color seen Fig.~\ref{fig:maplsew}i compared to Fig.~\ref{fig:maplsew}j). This asymmetry may be due to the role of the electric field in aiding the entry of protons to near-wake across the $+E_c$ pole. Similarly, the differential flux is asymmetric along $y$, with the flux in $-y$ (Fig.~\ref{fig:maplsew}g) being higher than in $+y$  (Fig.~\ref{fig:maplsew}h), closer to limb.  Since IMF lies in the $x$-$y$ plane with $y$-component always positive,  the asymmetry between $-y$ and $+y$ may be associated with the diffusion of solar wind parallel ($-y$) and anti-parallel to IMF ($+y$). Hence, for further analysis we have chosen five locations as shown in Fig.~\ref{fig:regions}. The location 1 is closer to $+E_c$ pole, location 2 is closer to $-E_c$ pole, location 3 is closer to $+y$ limb, location 4 is closer to $-y$ limb, and location 5 is in the central wake. While the location 5 consists of observations from spatial grid extend of 400 km $\times$ 400 km (in $y$-$z$ plane in LSwE co-ordinates), other locations are rectangular having spatial extents of 200 km  $\times$ 400 km. The locations 1 to 4 are at a distance of 1500 km to 1700 km from the centre of the wake. Due to the finite gyro-radius of protons in the solar wind, there is always a possibility for protons to be found in lunar wake close to the terminator.  Hence the observations very close to the terminator (limb observations) are excluded.

		      \begin{figure}

		        		 		    \includegraphics[width=30pc]{fig2}

		        		   		    \caption{Maps of wake protons in LSwE co-ordinate system. The top panel shows the number of observations in different planes whereas the bottom panel shows the observed differential flux. (a) The map of number of observations projected onto the $y-z$ plane, (b) number of observations in the $x-z$ plane ($V_{sw}-E_c$ plane) as viewed from the direction of $-y$, (c) same as (b) but viewed from the direction of $+y$, (d) number of observations in the $x-y$ plane  ($V_{sw}-B_{IMF}$ plane) as viewed from the direction of $+z$ ($+E_c$), (e)  same as (b) but as viewed from the direction of $-z$ ($-E_c$), (f) observed differential flux projected onto the $y-z$ plane, (g) observed differential flux projected onto the $x-z$ plane ($V_{sw}-E_c$ plane) as viewed from the direction of $-y$, (h)same as (g) but as viewed from the direction of $+y$ , (i) observed differential flux projected onto the $x-y$ plane  ($V_{sw}-B_{IMF}$ plane) as viewed from the direction of $+z$ ($+E_c$), (j) same as (i) but as viewed from the direction of $-z$ ($-E_c$).}

		        		   		   \label{fig:maplsew}
		        		   	\end{figure}

     Using the information on the energy and the direction of the particles observed by SWIM in the above mentioned five locations, the velocity distribution functions are computed in the aLSE co-ordinates and transformed to the solar wind rest frame. The velocity distribution functions are indeed functions of three dimensional velocity space, but to understand the population in a simple manner, we used the two dimensional velocity space, namely in  the directions parallel and perpendicular to the IMF ($v_\parallel$  and  $v_\perp$). Note that we employ the solar wind rest frame for this analysis. Indeed this frame is frequently used for the pitch angle (=arctan($v_\perp$/$v_\parallel$)) analysis. This frame is helpful for understanding the physical mechanisms of acceleration and the initial velocity vector of the protons, if they are produced near the Moon (such as exospheric ions).

     \begin{figure}
           		   \centering
           		 		     \includegraphics[width=30pc]{fig3}

           		   		    \caption{Map of differential flux of wake ions in the $y-z$ plane of the LSwE co-ordinate system, showing the 5 locations of interest (enclosed by red rectangular boxes). Location 1 at $+E_c$ limb, location 2 at $-E_c$ limb, location 3 at $+y$ limb, and location 4 at $-y$ limb, and location 5 at the central wake. The locations 3 and 4 are in the plane containing solar wind velocity and IMF.}
           		   		   \label{fig:regions}
           \end{figure}

    To understand the prevailing upstream solar wind conditions during the SWIM observations at locations 1 to 5 in lunar wake, the  velocity distribution of the upstream solar wind was also computed. The solar wind velocity data from the ACE spacecraft that has been time shifted to the location of Moon was  resolved into components parallel ($v_\parallel$) and perpendicular ($v_\perp$) to the IMF in aLSE co-ordinates.  The velocity components ($v_\parallel$  and  $v_\perp$) are binned into 50 km s$^{-1}$ $\times$ 50 km s$^{-1}$ grids. The frequency distribution, i.e., how many times the solar wind velocity was observed to be in a specific bin, for those days and timings where SWIM had observations over location-1 to location-5 is considered as the representative of the upstream solar wind condition. Fig.~\ref{fig:veldist1} shows the velocity distribution of the protons in the solar wind rest frame that are observed in locations 1 to 5 together with the upstream solar wind distribution in aLSE co-ordinate system.

     From Fig.~\ref{fig:veldist1}a--\ref{fig:veldist1}e, it can be seen that all the locations except location-5, have several velocity bins with significant values of  the distribution function  above the prevailing background.  The velocity bins which have value of the distribution function above 10$^{-13}$ s$^3$ m$^{-6}$ are considered to be significant above the background (1 count level). To identify the different populations of protons from the velocity distribution map, a selection criterium was employed in which any velocity bin is analysed in the following manner.  In the analysis, all the eight velocity bins surrounding a given bin (say center bin) are considered. Please note that all the bins referred here are in the velocity space ($v_\parallel$, $v_\perp$). The value of the distribution function in the center bin is compared with that of the surrounding eight bins and if the value in the surrounding bins are lower than that of the center bin by 50\%, the proton velocity distribution represented in the center bin together with the surrounding bins are considered as belonging to the same population.

      \begin{figure}
                        		   \centering

                        		 		     \includegraphics[width=30pc]{fig4}

                        		   		    \caption{ Top panel shows the velocity distribution of protons in the near lunar wake in the solar wind rest frame, and bottom panel shows the upstream solar wind distribution (from ACE) corresponding to the SWIM observations at each of the locations 1 to 5 . (a) velocity distribution of protons observed in location 1, (b) velocity distribution of protons observed in location 2, (c) velocity distribution of protons observed in location 3, (d) velocity distribution of protons observed in location 4, (e) velocity distribution of protons observed in location 5, (f) velocity distribution of upstream solar wind during the SWIM observations in location 1, (g) velocity distribution of upstream solar wind during the SWIM observations in lunar wake in location 2, (h)  velocity distribution of upstream solar wind during the SWIM observations  in lunar wake in location 3, (i) velocity distribution of upstream solar wind during the SWIM observations  in lunar wake in location 4, (j) velocity distribution of upstream solar wind during the SWIM observations  in lunar wake in location 5. Refer to Fig.~\ref{fig:regions} for the definition of the different locations.  `P1' to `P12' indicate the prominent proton populations at the different locations.

                        		   		    }

                        		   		   \label{fig:veldist1}
            \end{figure}

    If the value of the distribution function in any of the eight bins (say $vbin1$) is higher than that of the center bin by more than 50\%, then $vbin1$ is considered as the new center bin. The value of the distribution function in the eight bins surrounding $vbin1$ are compared with that of $vbin1$. This continues till all the eight velocity bins surrounding a center bin are found to have value less than that of the center bin (by 50\%). Once this is met, the velocity distribution represented from the first center bin till the final center bin are considered as belonging to a given population. According to this selection criterium, the prominent populations are marked in Fig.~\ref{fig:veldist1} (P1 to P12). For location 5, which is close to the central wake region, the signal strength is too low for any distinct proton population to be seen.

    In location 1 (Fig.~\ref{fig:veldist1}a), protons of population P1 have the values of ($v_\parallel\ ,v_\perp$) around (0, 150) km s$^{-1}$, those of P2 around (150, 350) km s$^{-1}$, and of P3  around (250, 50) km s$^{-1}$.   Comparison with the corresponding average upstream solar wind condition (Fig.~\ref{fig:veldist1}f) shows that protons belonging to P1 and P3 have velocities lower than that of solar wind ($\sim$400 km s$^{-1}$), whereas P2 have velocity comparable to that of solar wind. P1 comprises of protons of dominant  $v_\perp$ with negligible $v_\parallel$, P2 have $v_\perp$ comparable to that of solar wind with non-zero $v_\parallel$, and P3  have dominant $v_\parallel$ with negligible $v_\perp$.

    In location 2 (Fig.~\ref{fig:veldist1}b), three prominent proton populations are observed (P4 to P6). Protons belonging to P4 that have comparable $v_\parallel$ and $v_\perp$ appear as a  strip in the velocity space with $v_\parallel$ in the range $-200$ to $-450$  km s$^{-1}$ and $v_\perp$ in the range 150 to 350  km s$^{-1}$. P5 is centered around velocity bins of (0, 150) km s$^{-1}$, and P6 have $v_\parallel$ in the range 150 to 300  km s$^{-1}$ and $v_\perp$ in the range 200 to 400  km s$^{-1}$. Comparison with the corresponding upstream solar wind condition (Fig.~\ref{fig:veldist1}g) shows that while P4, and P6 may have velocities comparable to that of solar wind, P5 have velocities lower than that of solar wind.

     Three populations (P7 to P9) are observed in location 3 (Fig.~\ref{fig:veldist1}c) of which P7 have velocities centered around (200, 50) km s$^{-1}$,  P8 around ($-$50, 100) km s$^{-1}$, and P9  around (100, 350) km s$^{-1}$. Populations P7 and P8 have  velocities less than that of the corresponding upstream solar wind (Fig.~\ref{fig:veldist1}h), whereas P9 have velocities comparable to that of solar wind. In location 4 (Fig.~\ref{fig:veldist1}d), three populations (P10 to P12) are identified. Population P10 is centered around (200, 50) km s$^{-1}$, P11 around (100, 100) km s$^{-1}$, and P12 around ($-$50, 300) km s$^{-1}$. All of them have velocities lower than that of the upstream solar wind (Fig.~\ref{fig:veldist1}i).

    Further, the velocity distribution were separated based on the angle between the solar wind velocity and the interplanetary magnetic field in aLSE ($\theta_{IMF}$). Bins of 30{$^\circ$}\ with $\theta_{IMF}$ in the range 0{$^\circ$}\ to 30{$^\circ$}, 150{$^\circ$}\ to 180{$^\circ$}, 30{$^\circ$}\ to 60{$^\circ$}, 120{$^\circ$}\ to 150{$^\circ$}, 60{$^\circ$}\ to 90{$^\circ$}\ and 90{$^\circ$}\ to 120{$^\circ$}, are considered. Since there was no significant proton population in location 5 (Fig.~\ref{fig:veldist1}e), location 5 was not included in the further analysis. The IMF sorted velocity distribution for location 1 is shown in Fig.~\ref{fig:veldist2}. For  comparison, the distribution for the combined $\theta_{IMF}$ bins where  0{$^\circ$}\ to 30{$^\circ$}\ and 150{$^\circ$}\ to 180{$^\circ$}\ are combined, 30{$^\circ$}\ to 60{$^\circ$}\ and 120{$^\circ$}\ to 150{$^\circ$}\ combined, 60{$^\circ$}\ to 90{$^\circ$}\ and 90{$^\circ$}\ to 120{$^\circ$}\ combined are also shown in the bottom panel of Fig.~\ref{fig:veldist2}. The prominent proton populations are marked in the figure.

    	\begin{figure}
       	               		   \centering
       	               		 		     \includegraphics[width=30pc]{fig5}

       	               		   		    \caption{ The velocity distribution of wake protons at location 1 in the solar wind rest frame under different IMF angles of (a) 0{$^\circ$}--30{$^\circ$}, (b) 150{$^\circ$}--180{$^\circ$}, (c) 0{$^\circ$}--30{$^\circ$}\ and 150{$^\circ$}--180{$^\circ$}\ combined, (d) 30{$^\circ$}--60{$^\circ$}, (e) 120{$^\circ$}--150{$^\circ$}, (f) 30{$^\circ$}--60{$^\circ$}\ and 120{$^\circ$}--150{$^\circ$}\ combined, (g) 60{$^\circ$}--90{$^\circ$}, (h) 90{$^\circ$}--120{$^\circ$}, (i) 60{$^\circ$}--120{$^\circ$}\ combined bin. The white colored dotted vertical line in each panel is drawn at $v_\parallel= 0$. The prominent proton populations are marked in  the figure (X1, X2, X3, A1, A2, Y1, Y2, Y3, Y4, Y5, B1, B2, B3, B4, Z1, Z2, Z3, Z4, Z5, C1, C2, C3). Summary of the velocity components of the populations along with that of the  upstream solar wind  can be found in Table~\ref{table:VDF}.}

       	               		   		   \label{fig:veldist2}
       	               \end{figure}

   	The proton populations P1 to P3, seen in Fig.~\ref{fig:veldist1}a, show up for different bins of $\theta_{IMF}$ as seen from the Fig.~\ref{fig:veldist2}. X1 (Fig.~\ref{fig:veldist2}a) and X2  (Fig.~\ref{fig:veldist2}b) have similar velocity components centred around (50, 150) km s$^{-1}$ and clearly represent the distribution A1 (Fig.~\ref{fig:veldist2}c) for the combined $\theta_{IMF}$ of 0{$^\circ$}\ to 30{$^\circ$}\ and 150{$^\circ$}\ to 180{$^\circ$}. The population X3 is similar to A2. Similarly, for the $\theta_{IMF}$ of 30{$^\circ$}\ to 60{$^\circ$}\ and 120{$^\circ$}\ to 150{$^\circ$}, the distributions Y1 (Fig.~\ref{fig:veldist2}d) contributes to B2 (Fig.~\ref{fig:veldist2}f), Y2 (Fig.~\ref{fig:veldist2}d) contributes to B4 (Fig.~\ref{fig:veldist2}f), Y3 (Fig.~\ref{fig:veldist2}e) contributes to B1 (Fig.~\ref{fig:veldist2}f), Y4 (Fig.~\ref{fig:veldist2}e) contributes to B3 (Fig.~\ref{fig:veldist2}f),  and Y5 (Fig.~\ref{fig:veldist2}e) is also part of B3 (Fig.~\ref{fig:veldist2}f). Similar is the situation for the $\theta_{IMF}$ of 60{$^\circ$}\ to 90{$^\circ$}\ and 90{$^\circ$}\ to 120{$^\circ$}\ where C1  (Fig.~\ref{fig:veldist2}i) is contributed from Z1  (Fig.~\ref{fig:veldist2}g) and Z5  (Fig.~\ref{fig:veldist2}h); C3 (Fig.~\ref{fig:veldist2}i) from Z3 (Fig.~\ref{fig:veldist2}g); and C2 (Fig.~\ref{fig:veldist2}i) from Z2 (Fig.~\ref{fig:veldist2}g) and Z4  (Fig.~\ref{fig:veldist2}h).

   	 \begin{figure}
   	   	            		   \centering
   	   	            		 		     \includegraphics[width=30pc]{fig6}

   	   	            		   		    \caption{ The velocity distribution of protons in lunar wake in the solar wind rest frame for location 2 to location 4 under different values of $\theta_{IMF}$ (angle between solar wind velocity and IMF in aLSE co-ordinates). Each horizontal panel represents the distribution for a given location as indicated on the extreme right of the panels. Within a panel, each plot from left to right represents the velocity distribution for different bins of $\theta_{IMF}$, which is indicated on the top. (a) distribution for $\theta_{IMF}$ bin 1 at  location 2, (b) for $\theta_{IMF}$ bin 2 at location 2, (c) for $\theta_{IMF}$ bin 3 at location 2, (d) for $\theta_{IMF}$ bin 1 at  location 3,  (e) for $\theta_{IMF}$ bin 2 at location 3, (f) for $\theta_{IMF}$ bin 3 at  location 3, (f) for $\theta_{IMF}$ bin 1 at  location 4, (g) for $\theta_{IMF}$ bin 2 at  location 4, (h) for $\theta_{IMF}$ bin 3 at  location 4 (see Fig.~\ref{fig:regions} for the definition of the different locations). The $\theta_{IMF}$ bin 1 refers to 0{$^\circ$}--30{$^\circ$}\ and 150{$^\circ$}--180{$^\circ$}\ combined, $\theta_{IMF}$ bin 2 refers to 30{$^\circ$}--60{$^\circ$}\ and 120{$^\circ$}--150{$^\circ$}\  combined,  $\theta_{IMF}$ bin 3 refers to 90{$^\circ$}--120{$^\circ$}. The white colored dotted vertical line in each panel is drawn at v$_\parallel= 0$. The prominent proton populations are marked in red color from `D2' to `L2' and their velocity components  along with that of upstream solar wind are given in  Table~\ref{table:VDF}.   }

   	   	            		   		   \label{fig:veldist3}
   	   	            \end{figure}

   	Similar scenario was found to hold for location 2 to location 4 (not shown). Hence, the proton distribution for only the combined bins of $\theta_{IMF}$ are presented for locations 2 to 4 (Fig.~\ref{fig:veldist3}). The prominent proton populations identified  in each of the locations based on the selection criteria are marked in the Fig.~\ref{fig:veldist3} from D2 to L2.  A summary of the prominent proton populations in each of the locations 1 to 4 and their velocity components are given in Table~\ref{table:VDF}.

   	            \begin{table}

   	            \caption{Proton velocity distribution in location 1 to location 4 }
   	            \label{table:VDF}
   	            \centering
   	            \begin{tabular}{cccccc}
   	            \hline
   	            Location & Population & $v_\parallel^a$ \  &  $v_\perp^b$ \  & $|v_p|^c$\   & $|V_{sw}|^d$\\

   	            \hline
   	             1 & A1  & 0 & 150  & 150.0  & 400 \\
   	             1 & A2  & 200 & 200  & 282.8 & 400 \\
   	             1 & B1  & -100 & 100   & 141.4 & 400\\
   	             1 & B2  & 0 & 200   & 200.0 & 400\\
   	             1 & B3  & 150 & 200   & 250.0 & 400\\
   	             1 & B4  & 200 & 350   & 403.1 & 400\\
   	             1 & C1  & -50 & 100  & 111.8 & 400\\
   	             1 & C2  & 200 & 100  & 223.6 & 400\\
   	             1 & C3  & 200 & 350  & 403.1 & 400\\
   	             2 &  D1  & 50 & 200  & 206.1 & 350 \\
   	             2 &  D2  & -50 & 450  & 452.8 & 350 \\
   	             2 &   E1  & -50 & 100 & 111.8  & 350\\
   	             2 &   E2  & -350 & 250 & 430.11  & 350\\
   	             2 &   E3  & 100 & 150 & 180.3  & 350\\
   	             2 & F1  & 0 & 100  & 100.0 & 350 \\
   	             3 & G1  & -50 & 100    & 111.8 & 350 \\
   	             3 & G2  & 200 & 50    & 206.1 & 350 \\
   	             3 & G3  & 200 & 350    & 403.1 & 350 \\
   	             3 &  H1  & 0 & 200  & 200.0 & 350 \\
   	             3 &  H2  & -150 & 250  & 291.5 & 350 \\
   	             3 &  H3  & 100 & 350  & 364.0 & 350 \\
   	             3 &  H4  & 200 & 50  & 206.1 & 350 \\
   	             3 &  I1  & -100 & 50  & 141.4 & 350 \\
   	             3 &  I2  & 0 & 300  & 300.0 & 350 \\
   	             4 &  J1  & 50 & 100  & 111.8 & 450 \\
   	             4 &  K1  & 150 & 150    & 212.1 & 450 \\
   	             4 &  L1   & 200 & 50    & 250  & 450 \\
   	             4 &  L2  & 150 & 300  & 335.4 & 450 \\

   	             \hline
   	            \end{tabular} \\
   	            \centering {\small All velocity values in  km s$^{-1}$} \\
   	            \flushleft {$^a$\small velocity of wake protons parallel to IMF in the solar wind rest frame }
   	            \flushleft {$^b$\small velocity of wake protons perpendicular to IMF in the solar wind rest frame }\\
   	            \flushleft {$^c$\small velocity magnitude of wake protons in solar wind rest frame }\\
   	            \flushleft {$^d$\small solar wind velocity in aLSE co-ordinates }

   	            \end{table}

\section{Discussion}

		 The source of protons in the near-lunar wake can be categorized into two. The first is the direct solar wind entry \citep{Nishino09a, Futaana10b, Dhanya13}, and the second is the solar wind after modification due to interaction with lunar surface and magnetic anomalies \citep{Nishino09b, Wang10}. The term `direct' is used to indicate the absence of interaction with lunar surface or magnetic anomalies. The processes which are known for the direct entry are: (1) protons diffusing along the IMF (parallel or anti-parallel to IMF) which can be termed as parallel entry \citep{Futaana10b},  (2) increase in Larmor radii due to the wake boundary electric field \citep{Nishino09a}, and (3) protons from the tail of the solar wind velocity distribution having large gyro-radii \citep{Dhanya13}. The scattering of the solar wind upon interaction with the lunar surface or magnetic anomalies and their subsequent trajectory under IMF and convective electric field enable the protons of the second category to enter the near lunar wake \citep{Nishino09b, Wang10}.

		In the solar wind rest frame, the parallel entry protons will have dominant $v_\parallel$ with almost zero or much smaller $v_\perp$.   The magnitude of the velocity ($v_p$) may be less than that of solar wind (solar wind speed in aLSE). It is to be noted that although \cite{Futaana10b} discussed the observation when IMF was perpendicular to the solar wind velocity vector ($\theta_{IMF} \sim 90${$^\circ$}), this mechanism can operate for other IMF orientations as well, except for magnetic aligned flow ($\theta_{IMF} \sim 0${$^\circ$}).  For convenience, we use the term `Entry-1' for this process, in further discussion. Let's recall that in the LSwE co-ordinates, the IMF is confined in the $x$-$y$ plane with $y$-component always positive and V$_{sw}$ is along $-x$. Hence, for IMF angles of 0{$^\circ$}\ to 30{$^\circ$}, and 150{$^\circ$}\ to 180{$^\circ$}, these protons may not be able to reach location 1, which is closer to $+E_c$ ($+z$) pole. This applies for location 2 also, which is closer to  $-E_c$ ($-z$) pole. The parallel entry protons will be able to reach location 3 (along $+y$) and location 4 (along $-y$) for all IMF angles except  $\theta_{IMF} \sim$ 0{$^\circ$}. The populations `G2' and `H4' in location 3, with dominant $v_\parallel$ and negligible $v_\perp$ are most likely due to Entry-1. The population `I1' in location 3 and `L1' in location 4 may also be associated with  Entry-1.

		When the solar wind protons enter the lunar wake due to their finite gyro-radius aided by the wake boundary electric field, they travel in a direction perpendicular to IMF \citep{Nishino09a}. In the solar wind rest frame, these protons are expected to have a dominant $v_\perp$ component and may have a small  component of thermal velocity parallel to the magnetic field. Due to the wake boundary electric field, $v_\perp$ will be enhanced above the thermal velocity. These protons may be characterized with $v_\perp > v_\parallel$, and since $v_\parallel$ is expected to be negligible, it can be considered that $v_\parallel$ $< 0.25 \times v_\perp$. The velocity of such protons is expected to be lower than the solar wind bulk velocity. Although this mechanism has been reported for $\theta_{IMF} \sim 90${$^\circ$}, this mechanism is likely to be active for other IMF orientations. For convenience, we use the term `Entry-2' for this process in further discussions. `Entry-2' is same as `Type-I', defined in \cite{Nishino09b} for the mechanism described in \cite{Nishino09a}. The protons of Entry-2 can reach the $-E_c$ and $+E_c$ poles (locations 1 and 2) for 0{$^\circ$}\ $\le \theta_{IMF} \le$ 90{$^\circ$}. These protons may access locations 3 and 4 for smaller values of $\theta_{IMF}$ ($\sim$ 0{$^\circ$}), whereas for larger values of $\theta_{IMF}$, these protons will start to diffuse along the IMF into the wake. Also, Entry-2 protons may not access the central wake, i.e., location 5. The populations A1, B2, C1 in location 1; D1, E1, F1 in location 2; and G1, H1 in location 3 have the  characteristics of velocity distribution to be associated with Entry-2.

	     The protons which enter the lunar wake by virtue of their large  gyro-radius  \citep{Dhanya13} from the high-energy tail of solar wind velocity distribution (having large thermal velocities) are expected to have dominant $v_\perp$. Such protons have gyro-radii larger than the lunar radius in the solar wind. Since the gyro-radius depends on the IMF, which is a variable, the perpendicular velocity ($v_\perp$) of these protons can be either higher or lower than that of solar wind bulk speed depending on the strength of IMF and the magnitude of V$_{sw}$. For a typical solar wind condition of 400 km s$^{-1}$ bulk speed and 5 nT IMF, the value of $v_\perp$ could be be higher than V$_{sw}$ for the protons to have gyro-radii larger than lunar radius. If IMF is weak, say 1 nT, then for a smaller $v_\perp$ itself  ($\sim$200 km s$^{-1}$), the gyro-radius of protons can be  larger than lunar radius. Since these protons have larger thermal velocity, they may have significant $v_\parallel$ component also. Although this mechanism have been observed during magnetic field aligned flow ($\theta_{IMF} \sim 0${$^\circ$}), this can be active for other IMF orientations as well, although the flux may be lower. We use the term `Entry-3' for this process. Since protons of Entry-3 depend solely on their gyro-radii to enter into the wake, they may access all the five locations. The populations A1, A2, B1, B2, B3, C2 in location 1; D1, D2 , E1, E3, F1 in location 2; G1, G3, H1, H2, H3, I1, I2 in location 4; and J1, K1, L2 in location 4 have the characteristics of Entry-3 protons.  To assess the contribution of Entry-3 in the above populations, we considered the magnitude of IMF that was prevailing during the observation. From the IMF magnitude, the minimum  $v_\perp$ that is required for the gyro-radius of protons to be equal to that of lunar radius, is estimated. This estimated $v_\perp$ is compared against the observed $v_\perp$ of different populations. This analysis showed that Entry-3 can play a role for the populations B2, B3 in location 1; D2, E1, E3, F1 in location 2; G1, G3, H1, H2, I2 in location 3; and J1, K1 in  location 4. Entry-3 may contribute partially for C2, and L2 because of the low IMF condition during some of the observation of these populations.

		It has been observed that  0.1--1\% of the solar wind protons scatter back to space upon interaction with the lunar surface \citep{Saito08}. Also, $<$50\% of solar wind protons scatter upon interaction with the lunar magnetic anomalies \citep{Saito10, Lue11}. The protons scattered from anomalies are found to have velocities almost similar to that of solar wind but heated up \citep{Saito10, Lue11}. In solar wind rest frame, such protons will have similar velocity distribution as that of surface scattered protons. The trajectories of these protons would be controlled by IMF and the convective electric field \citep{Holmstrom10} and some of which can eventually access the near-lunar wake \citep{Nishino09b, Wang10}. We refer to such an entry mechanism as `Entry-4'. Although Entry-4 is similar to the Type-II mechanism reported by \cite{Nishino09b} with reference to the surface scattered protons, Entry-4 includes protons scattered by magnetic anomalies as well. In the solar wind frame, the backscattered protons will have velocities in the range $V_{sw}$ to $2\times V_{sw}$ considering the extreme scattering angles of 90{$^\circ$}\ and 180{$^\circ$}, and assuming negligible energy loss upon scattering.  In the Moon reference frame, since the backscattered protons access the wake by travelling along $+E_c$ and crossing the $+E_c$ terminator \citep{Nishino09b}, they are not likely to be seen in location 2, whereas they can access location 3 and location 4 for oblique IMF orientations.  The populations B4, and C3 in location 1 with dominant $v_\perp$ and velocities comparable to that of the background solar wind are most likely due to Entry-4. The population G3, H3, I2 in location 3 also have the characteristics associated with  Entry-4. The population D2 in location 2 also have the characteristics of Entry-4 protons, but the location is close to $-E_c$ pole and hence Entry-4 is not expected.

	    The protons which are forward scattered at the terminator  would also be able to reach the lunar wake region \citep{Wang10}, where forward scattered protons closer to the $-E_c$ pole enter the nightside.  We use the term `Entry-5' for such a process. Entry-5 is used here for the forward scattered protons close to the terminator in any region (not only $-E_c$ pole). In the solar wind rest frame, the forward scattered protons will have velocities in the ranging from zero to $V_{sw}$ for the two extreme scattering angles 0{$^\circ$}\ and 90{$^\circ$}, assuming negligible energy loss upon scattering. Also, such protons are expected to have dominant $v_\perp$ as seen from the solar wind frame. Since the forward scattered protons can access the wake across $-E_c$ terminator \citep{Wang10}, they can be seen in location 2. The populations A1, A2, B1, B2, B3, C1 in location 1; D1, E1, E3, F1 in location 2; G1, H1, H2, I1 in location 3; and J1, K1, L2 in location 4 have the characteristics to be associated with Entry -5.

	  	The summary of the various entry mechanisms discussed above, the expected velocity distribution of protons in solar wind rest frame for each mechanism and the observed populations which are most likely associated with each of the entry mechanisms are provided in Table~\ref{table:summary}. It is seen that for several populations, more than one entry mechanism may play a role.

		\begin{table}
		\caption{Mechanisms of entry of solar wind protons in the near-lunar wake,  expected velocity distribution in solar wind rest frame, and the observed populations which are most likely associated with each of the entry mechanisms}
		\label{table:summary}
		\centering
		\begin{tabular}{llll}
		\hline

		 Process  & References & Expected velocity distribution & observed population \\
		 \hline

		 Entry-1 & \cite{Futaana10b}  & Dominant $v_\parallel$ ($v_\perp \sim$ 0); $v_{p} << V_{sw}$ & G2, H4, I1, L1  \\[5pt]

		 Entry-2 & \cite{Nishino09a}  & Dominant $v_\perp$ ($v_\parallel \sim$ 0); $v_{p} < V_{sw}$  & A1, B2, C1, D1, E1, F1, \\
		 & & & G1, H1 \\[5pt]
		 Entry-3 & \cite{Dhanya13}  & Dominant $v_\perp$; $v_{p}$ may be greater  & B2, B3, D2, E1, E3, F1, \\

		 &  & or smaller than $V_{sw}$ & G1, G3,
		 H1, H2, I2, J1, \\
		& & & K1, C2*, L2*  \\[5pt]
		 Entry-4 & \cite{Nishino09b},  & Dominant $v_\perp$ ; $v_{p}: \sim V_{sw} \ to\  2* V_{sw}$ & B4, C3, G3, H3, I2 \\

		 Entry-5 & \cite{Wang10}     & Dominant $v_\perp$; $v_{p} << V_{sw}$ &  A1, A2, B1, B2,
		 B3, C1, \\
		 & & & D1, E1, E3, F1, G1, H1, \\
		 & & & H2, J1, K1, L2 \\[5pt]
		 \hline
		\end{tabular}
		\flushleft {* Partially due to the low IMF condition during some of the observation of these populations \\
		$v_{p}$ =  velocity of the wake protons \\
		V$_{sw}$ = solar wind bulk velocity}
		\end{table}

		To gain more insight into the entry process, we have carried out the backtracing of the protons belonging to different populations. The trajectory of the protons are computed backwards in time from their observed position in the lunar wake (in aLSE coordinates) under the Lorentz force. The position where the protons are observed in the lunar wake, and their observed velocities (in a given energy and direction bin of SWIM) are used as the initial values. Since the magnetic field in the wake has been found to increase to 1.5 $\times $ B$_{IMF}$ \citep{Colburn67}, for trajectory calculations, we used  magnetic field value of 1.5 $\times $ B$_{IMF}$  inside the wake region and 1.0 $\times $ B$_{IMF}$ outside the wake. Regarding the electric field, outside the wake, the protons experience the convective electric field of solar wind ($E_c =-V_{sw} \times B_{IMF}$). Inside the wake, protons will experience an additional electric field - the wake boundary electric field \citep{Halekas05,Kallio05,Nishino09a}. Similar to that discussed in \cite{Nishino09a} which agrees with the observations \citep{Halekas05}, we used a wake boundary electric field value of 0.7 mV m$^{-1}$ which acts in a region of width 0.25$\times$R$_L$  from the terminator, where $R_L$ refers to the lunar radius. Fig.~\ref{fig:Ewake} illustrates the geometry of the wake electric field used in the backtracing. As seen from Fig.~\ref{fig:Ewake}, the electric field is directed inward from the terminator towards the Sun-Moon line  \citep{Nishino09a}.

			To solve the Lorentz equation numerically, Euler's method was used with a time step of 0.001 s. The model calculates the position and velocity of the protons back in time (in aLSE) until proton trajectory either intersect the lunar surface or travel a sufficiently larger distance ($>$ 5000 km) upstream. In other words, calculations terminate when either the magnitude of the position vector of the protons becomes less than or equal to the radius of the Moon (1738 km) or exceeds 5000 km. For the solar wind velocity and IMF, data from ACE satellite (time shifted to the location of Moon) was used. Backtracing was not done for the populations which were considered to be associated with Entry-1 (G2, H4, I1, L1).

		   \begin{figure}
		                         		   \centering
		                         		 		     \includegraphics[width=25pc]{fig7}

		                         		   		    \caption{ Illustration of the lunar wake boundary electric field (E$_{wake}$) taken in the proton backtracing model. The outer circle represents the lunar terminator (wake boundary). E$_{wake}$ is shown by red arrows from the wake boundary pointing inwards towards the Sun-Moon line. E$_{wake}$  acts in the shaded region of width  $0.25 \times R_L$ from the wake boundary, where R$_L$ refers to the lunar radius. The inner circle has a radius of 0.75$\times$ R$_L$.   The magnitude of E$_{wake}$ is 0.7 mV m$^{-1}$. This scheme is similar to that discussed in \cite{Nishino09a} and agrees with the observations \citep{Halekas05}. The $x$, $y$, $z$ axes are as defined in the aLSE co-ordinate system, where $x$-axis points into the plane of the paper.  }

		                         		   		   \label{fig:Ewake}
		                         \end{figure}

		\begin{figure}
		                     		   \centering
		                     		 		     \includegraphics[width=40pc]{fig8}

		                     		   		    \caption{ Backtracing results in aLSE co-ordinates. (a)--(c): for population A1 in location 1, (d)--(f): population G3 in location 3, (g)--(i): population H3 in location 3, (j)--(l): population L2 in location 4.
		                     		   		    The left most panels (a), (d), (g), (j) show projection in the $x-y$ plane; middle panels (b), (e), (h), (k) show projection in the  $x-z$ plane; and right most panels (c), (f), (i), (l) represent projection in $y-z$ plane. The protons are traced back based on their observed location, energy and direction. The color bar represents the counts of the protons (observed in the specific energy and direction bins of SWIM) accumulated over the spatial grids of size 100 km $\times$ 100 km, at the end of backtracing. The protons which hit the nightside surface are unrealistic. The value of magnetic field in the wake is assumed to be 1.5$\times$ B$_{IMF}$ \citep{Colburn67}. In addition to the convective electric field of solar wind, a wake boundary electric field of 0.7 mV m$^{-1}$ has been considered (see Fig.~\ref{fig:Ewake} for details).  }
		                     		   		   \label{fig:backtraceCG}
		                     \end{figure}

		The results of the backtracing for the four populations A1, G3, H3, and L2 are shown in Fig.~\ref{fig:backtraceCG}. The plots are generated by binning the position co-ordinates of the protons at the end of backtracing into grids of size 100 $\times$ 100 km and are projected onto different 2-D planes ($x$-$y$, $x$-$z$, and $y$-$z$) in aLSE co-ordinates. The counts observed, in a particular energy and direction bin of SWIM, are accumulated over the spatial grids at the end of backtracing and is represented as color bar. The trajectories which terminate on the nightside surface should be ignored since they are unrealistic.

		From Figs.~\ref{fig:backtraceCG}a to ~\ref{fig:backtraceCG}c, it can be seen that for population A1, almost all particles goes to the solar wind (99.3\%) with a minor contribution from the dayside surface (0.6\%) close to the terminator. The value 99.3\% represents the ratio of observed counts which terminate in solar wind to the sum of counts which terminate in the solar wind and on the dayside surface, at the end of backtracing. Similarly, 0.6\% represents the ratio of observed counts which terminate on the dayside surface to the sum of counts which terminate in solar wind and on the dayside surface, at the end of backtracing.  Thus, the source of A1 is most likely Entry-2 with minor contribution from Entry-5, as expected from the velocity distribution.

		Figs.~\ref{fig:backtraceCG}d to ~\ref{fig:backtraceCG}f show that the population G3 has significant contribution (31\%) from the surface. The protons scattered from surface (or magnetic anomalies) may contribute significantly to G3. The mechanisms could be Entry-4 (from surface) and Entry-3 (from solar wind) as expected from the velocity distribution. Similarly, for the population H3 also (Figs.~\ref{fig:backtraceCG}g to \ref{fig:backtraceCG}i), backtracing shows significant contribution from the dayside surface (17\%). The mechanism could be Entry-4 which agrees with the inference drawn from the velocity distribution. Whereas both the velocity distribution and backtracing suggested the contribution from Entry-4, backtracing has shown that the dominant source is solar wind. The velocity distribution for H3 do not support Entry-2 as the source and Entry-3 is also not expected to contribute based on the prevailing IMF. Thus, the process by which solar wind contribute to H3 is left open. Population L2 (Figs.~\ref{fig:backtraceCG}j to \ref{fig:backtraceCG}l), have dominant contribution from solar wind with minor contribution (0.2\%) from surface. As discussed before, L2 was considered to be associated with Entry-5 and Entry-3 (partially) based on the velocity distribution. Backtracing shows that Entry-3 may still contribute whereas  Entry-5 may make only minor contribution to L2.

		Similar backtracing carried out for other populations (results not shown), indicated that the population A2 has roughly equal  contributions from the solar wind (43.4\%) and the dayside surface (56.5\%). As discussed before, neither Entry-2 nor Entry-3 plays a role for A2. Thus the mechanism for the contribution from solar wind is not clear.  The surface contribution is more likely associated with Entry-5. For other populations in  location 1, backtracing showed that the source for B1, B2, B3, B4, C1, C2 and C3 is mainly solar wind with almost no contribution from surface.
		For B1, the velocity distribution indicate Entry-5 as possible mechanism whereas backtracing suggest no contribution from the surface.  The population B2 is more likely associated with Entry-2 and Entry-3, B3 with Entry-3, and C1 with Entry-2. As discussed before, Entry-3 may partially account for population C2, and hence there may be some other unknown entry mechanism that also contribute to C2.

		Regarding B4 and C3 in location 1, they have significant $v_\parallel$ and  $v_\perp$, and the velocities are comparable to that of solar wind. Also, the ($v_\parallel$, $v_\perp$) components are similar to that of solar wind. They were suspected to be associated with Entry-4 as inferred from the velocity distribution. However, backtracing suggested that they are purely of solar wind origin without any surface contribution (i.e., Entry-4 not supported). Thus their source remains unknown. However, since their velocity components are similar to that of solar wind, they could be lunar exospheric H$^+$ that are picked up by the solar wind (closer to the terminator) above the lunar surface. However, a detailed analysis is required to confirm these and is the scope for future work.

		In location 2, backtracing showed that populations D1 has minor contribution from surface ($<$1\%), and are dominantly of solar wind origin. They could be due to Entry-2 with minor contributions from Entry-5. Backtracing for D2 suggests that the the major source is solar wind with significant contribution from surface (21.5\%). The entry mechanism from solar wind could be Entry-3, whereas the mechanism for the source from the surface cannot be explained. Similar to D1, E1 also have dominant contribution from solar wind (99.5\%) with minor contribution from surface. The source of E1 could be Entry-2, Entry-3 and minor contribution from Entry-5 as expected. For E3, significant contribution is seen from surface ($\sim$7\%) and could be associated with Entry-3 as major process with significant role by Entry-5. F1 have solar wind as dominant source (98\%) and also contribution from surface. F1 could be due Entry-2, Entry-3 and with significant contribution from Entry-5.

		The population E2 in location 2, which appears as a strip in the velocity distribution map,  has comparable $v_\parallel$ and $ v_\perp$, and the  velocity magnitude is comparable to that of solar wind. The backtracing for E2 showed minor ($<$2\%) contribution from surface and dominant contribution from solar wind. For the surface contribution, Entry-4 across $-E_c$ pole is unlikely (even if the protons are from magnetic anomaly). Thus, the source for the surface contribution for E2 is not clear. For the solar wind part, Entry-3 may be the likely process.

		In location 3, backtracing suggests that populations G1 and H1 have minor contribution from surface ($<$1\%), and  is dominantly of solar wind origin. Entry-2, Entry-3, and Entry-5 can be associated with these populations. For H2, backtracing showed major contribution from solar wind, likely to be due to Entry-3, and significant contribution from surface (11\%) which may be due to Entry-5. Backtracing for I2 suggests major contribution from solar wind  which may be due to Entry-3 with significant contribution from surface ($\sim$2.5\%), which could be due to Entry-4, as expected from the velocity distribution.

		In location 4, for J1 backtracing shows solar wind as the source with no contribution from the surface. The entry mechanism for solar wind protons could be associated with Entry-3. For the population K1, the dominant source appears to be solar wind (likely to be associated with Entry-3) and the contribution from surface is negligible ($<$1\%) which can be associated with Entry-5.

		In summary, of the 28 populations of protons in the near-lunar wake observed by SWIM, several populations are associated with known processes, such as Entry-1, Entry-2, Entry-3, Entry-4 and Entry-5.  There are a few populations whose entry process could not be explained by the known mechanisms. These include direct solar wind contribution for A2, B1, B4, C3, E2, H3, and dayside surface contribution for D2. Since Entry-3 may partially account for populations C2 and L2, there may be some other unknown entry mechanism that also contribute to these populations. Table~\ref{table:summaryVDFBT} provides a summary of the results on the entry mechanisms associated with the different populations that are arrived at based on the velocity distribution and backtracking.

		   It is to be noted that except parallel entry, all other  known entry mechanism involve the gyration of the solar wind protons around IMF, either by virtue of large thermal velocity or by experiencing additional electric field (convective or at wake boundary) and their trajectories enable the protons to enter the near-lunar wake.

		   \begin{sidewaystable}

		   \caption{Entry mechanisms expected from velocity distribution, the source identified from backtracing, and inferences on the entry mechanisms of the different populations at locations 1--4 compared with that of backtracing}
		   \label{table:summaryVDFBT}
		   \centering
		   \begin{tabular}{lllll}
		   \hline

		   Location & population  & Entry mechanism from &  Result from backtracing* & Inference  \\
		   & &  velocity distribution&  &\\
		    \hline

		    1 & A1 &  Entry-2, Entry-5 & solar wind (99.3\%)  & Entry-2, Entry-5\\
		    1 & A2 &  Entry-5 & solar wind (43.4\%)  & Entry-5 and unknown mechanism\\
		    & & & &  for the direct solar wind entry \\
		    1 & B1 &  Entry-5 & solar wind (100\%) & mechanism unknown\\
		     1 & B2 &  Entry-2, Entry-3, Entry-5 & solar wind (100\%) & Entry-2,Entry-3\\
		      1 & B3 & Entry-3, Entry-5 & solar wind (100\%) & Entry-3\\
		      1 & B4 & Entry-4 &  solar wind (100\%) & unknown\\
		      1 & C1 & Entry-2, Entry-5 &  solar wind (100\%)  & Entry-2\\
		    1 & C2 & Entry-3** &  solar wind (100\%) & Entry-3 and unknown mechanism\\
		    1 & C3 & Entry-4 &  solar wind (100\%) & unknown \\
		    2 & D1 & Entry-2, Entry-5 &  solar wind (96.7\%)  & Entry-2, Entry-5\\
		    2 & D2 & Entry-3 &  solar wind (78.5\%)  & Entry-3, and source from the  \\
		    & & & & dayside surface is unknown\\
		    2 & E1 & Entry-2, Entry-3, Entry-5 &  solar wind (99.5\%)  & Entry-2, Entry-3, Entry-5\\
		    2 & E2 & unknown  &  solar wind (98.3\%)  &  process unknown\\
		    2 & E3 & Entry-3, Entry-5  &  solar wind (93\%)  & Entry-3, Entry-5\\
		    2 & F1 & Entry-2, Entry-3, Entry-5  &  solar wind (98\%)  & Entry-2, Entry-3, Entry-5\\
		    3 & G1 & Entry-2, Entry-3, Entry-5  &  solar wind (99.6\%)  & Entry-2, Entry-3, Entry-5\\
		    3 & G2 & Entry-1 &  --- & Entry-1\\
		    3 & G3 & Entry-3, Entry-4  &  solar wind (69\%)  & Entry-3, Entry-4\\
		    3 & H1 & Entry-2, Entry-3, Entry-5  &  solar wind (98.6\%) & Entry-2, Entry-3, Entry-5\\
		    3 & H2 & Entry-3, Entry-5  &  solar wind (89\%)  & Entry-3, Entry-5\\
		    3 & H3 & Entry-4  &  solar wind (83\%)  & Entry-4 and unknown mechanism\\
		     & & & &  for the direct solar wind entry \\
		    3 & H4 & Entry-1  & --- & Entry-1\\
		    3 & I1 & Entry-1  & ---  & Entry-1\\
		    3 & I2 & Entry-3, Entry-4  &  solar wind (97.5\%) & Entry-3, Entry-4\\
		    4 & J1 & Entry-3, Entry-5  &  solar wind (100\%) & Entry-3\\
		   4 & K1 & Entry-3, Entry-5  &  solar wind (99\%) & Entry-3, Entry-5\\
		   4 & L1 & Entry-1  &  solar wind (99.9\%)  & Entry-1\\
		   4 & L2 & Entry-3**, Entry-5  &  solar wind (99.8\%) & Entry-3 and unknown mechanism, Entry-5\\

		    \hline
		   \end{tabular}
		   \flushleft {\footnotesize * The contribution from solar wind is given. The value in brackets represents the ratio (in percentage) of the observed proton counts which terminate in solar wind to the sum of the counts which terminate in the solar wind and the dayside surface, at the end of backtracing. The difference of this value from 100\% represents the contribution from the dayside surface.\\
		   ** Partially due to the low IMF condition during some of the observation of these populations }

		   \end{sidewaystable}

\section{Conclusion}

Using the observations by SWIM sensor of the SARA experiment on Chandrayaan-1, the velocity distributions of the protons in the near-lunar wake (100 to 200 km from the lunar surface) are computed in the solar wind rest frame.  The velocity distributions were further sorted according to the angle between the upstream solar wind velocity and IMF. The distributions are not identical for different IMF orientation, which suggests the control of IMF in the proton entry process. The protons were found to enter the lunar wake parallel as well as perpendicular to the direction of IMF.  Most of the observed protons have velocities lower than that of the solar wind, and a few populations have velocity comparable to that of solar wind. From the velocity distribution, several population of protons were identified based on the selection criterium. The possible mechanism for the proton entry to the near wake associated with these populations were inferred from the characteristics of velocity distribution. The mechanisms include diffusion of solar wind protons into the wake along IMF, by virtue of gyro-radii of solar wind protons and scattering of solar wind protons from the dayside lunar surface or from magnetic anomalies. To gain more insight into the source of these populations,  the trajectory of the protons are computed back in time (backtracing) under the influence of IMF, convective and wake boundary electric field. For most of the populations, the source of the protons  obtained from backtracing agree with the inferences drawn from the velocity distribution. There are few populations whose entry mechanism could not be explained by the known processes.

\flushleft \textbf {Acknowledgments}\\[5pt]
\justify {We thank the ACE SWEPAM instrument team, ACE MAG instrument team and the ACE Science Center for providing the ACE data. This work has been supported by the Indo-Swedish International Collaborative Research Grant by the  Swedish International Developement Corporation Agency (SIDA). The efforts at Space Physics Laboratory of Vikram Sarabhai Space Centre are supported by Indian Space Research Organisation (ISRO). The effort at the University of Bern was supported in part by ESA and by the Swiss National
Science Foundation.}

\flushleft \textbf {References}

redpajama_set_name: RedPajamaArXiv


INTRODUCING THE LIMITED MINI 60 YEARS EDITION.
2019 is a big year for MINI as we celebrate turning 60 years young. We're marking this auspicious occasion with the release of the MINI 60 Years Edition. Limited to only 20 vehicles.
From its heritage rich British Racing Green finish, exclusive Pepper White roof and wing mirrors and exclusive 17" wheel 60 Years alloys, this is one vehicle that is both traditional yet contemporary. Numbers are strictly limited, so do not miss the opportunity to explore more corners and become part of our history with a vehicle like this.
An original that constantly reinvents itself – firmly rooted in tradition yet always open to change: this is MINI, 60 years after the launch of the small British car that brought worldwide popularity to unique properties such as go-kart feeling and the creative use of space.
To mark this round anniversary, the premium automobile manufacturer presents a design model that highlights both its British origins and the agile MINI character.
With design and equipment features that are both high-quality and exclusive, the MINI 60 Years Edition expresses the brand's sporting spirit – something that is a constant presence even in everyday urban traffic.
The exterior paint finish in British Racing Green offers a particularly clear expression of the premium small car's character and origins.
The design model's striking 60 Years logo appears not just on the left-hand bonnet stripe but also on the side scuttles of the turn indicators and on the door sill finishers at the driver and front passenger doors. Inside the car it can also be seen on the front headrests and the steering wheel. The anniversary design can also be seen in the LED logo projection which is visible when the driver's door is opened.


Meet the Toolmaker is an exclusive annual event that is organised and run by the GTMA and The BPF. Delivering the opportunity to meet the UK's finest mould tool manufacturers. Phoenix were thrilled to exhibit alongside the likes of Amtek Plastics UK, ND Precision Products and Petford Tools. Showcasing our extensive mould tooling services to the vast number of the visitors at the event.
This year's event was held at The Manufacturing Training Centre in Coventry, a truly outstanding venue that showcases British manufacturing and the innovative advances in technology.
Footfall was strong from the outset and the team from Phoenix enjoyed speaking with both existing and potential customers. Taking the opportunity to highlight the recent investments in both plant and staff which enhances our tooling services.
Attendees to the event were able to benefit further from a selection of presentations from key industry speakers as well as a tour of the MTC's Additive Manufacturing Centre and Fanuc Facility. The tours were truly inspirational, with small groups of visitors being guided around the facility and given brief presentation on the processes that are being researched and developed.
The atmosphere through-out the day was at an all time high, with everyone making the most of the business networking opportunity. As we all face uncertainty in the wake of Brexit, it was both encouraging and uplifting to see such positivity surrounding our UK engineering and plastics industry.
If you attended the event and didn't get a chance to speak to us, or simply want to know more about our services, please contact us. We're happy to discuss what we can offer you and see how we can work together to the benefit of your business. Our expert team has decades of experience and we pride ourselves on outstanding customer service.


Being concerned for the poor is a good thing, obviously! God commands it, and Jesus' life models it. Nevertheless, Jesus reminds us not to lose sight of the big picture. An unnamed woman had just entered the room with an outrageously expensive bottle of perfume. Boldly, shockingly, scandalously, she broke open the container and poured the contents on Jesus' head. The onlookers were indignant. "What a waste!" they said. "You could have sold that perfume for a year's wages and given the money to the poor!" And they rebuked her harshly.
But Jesus saw it differently. This woman recognized who Jesus was and what He was about to do. In an intimate act of worship, she acknowledged Him and gave her most valuable treasure to Him in an act of lavish adoration. Jesus received her love and praised her for seeing what the others couldn't see.
This story raises an important question: Are there ever times when God might want you to say no to the good so you can say yes to the best? Is your spiritual life ever out of balance? For example, do you ever get so busy serving people that you don't have time to worship God? Or does your passion for studying God's Word ever take priority over your pursuit of heart change and spiritual transformation?
Serving the poor, worshiping, studying the Scriptures, developing spiritual gifts, becoming more like Jesus—these are all important parts of following God. But one is not more important than another. Ask God to show you where your sense of timing or balance may be off in your expression of any of these, then invite Him to help you grow in the areas that are neglected or weak. Then take it a step further: If you have criticized others (aloud or even in your thoughts) for not being more like you in the way you follow God, ask God's forgiveness, and if appropriate, theirs as well.


text:
First Avenue	First Avenue
2020 © First Avenue Group Ltd
work@firstavenue.agency
Welcome Churches
Welcome Churches mobilises organisations across the nations to create opportunities in welcoming refugees and asylum seekers. They express their love and support by giving Welcome Boxes to refugees. Through their work, they bring hope to those who are not yet at home in the United Kingdom.
The goal was to create a website and a network system that connects participating organisations with refugees. Our developers built a platform that fits perfectly with their day to day operations, and enabled them to triple the number of the previous signups.
Mail Campaign
2020 © First Avenue Group Limited | Terms & Conditions

redpajama_set_name: RedPajamaCommonCrawl


text:
The Groove Radio Show
Slightly Stoopid Winter Tour 2011 Dates Announced
Keller Williams Announces Winter 2010 Tour and new Children's Book
Jake Shimabukuro's "Go For Broke" Pays Tribute to WWII Vet's Legacy
On 'Peace Love Ukulele' (out January 4th from Hitchhike Records), Jake Shimabukuro displays his customary "brilliance and brio" (NPR) on the ukulele with "Go...
Old Settler's Music Festival 2011 Avett Brothers, Emmitt-Nershi, Sam Bush, Trampled By Turtles
The 2011 partial lineup includes The Avett Brothers, Sam Bush, Tim O'Brien, Emmitt-Nershi Band (featuring Drew Emmitt from Leftover Salmon and Bill Nershi from...
Legendary Blues Collaboration to Celebrate 100 Years of Robert Johnson
How do you throw a 100th birthday bash for the most influential bluesman that ever lived? If you're Big Head Todd and The Monsters,...
Snoe.down Returns 3/25 – 3/27/10 to Killington Resort in Vermont
Snoe.down, the all-ages winter music & sports festival hosted by moe., returns to central Vermont and Vermont's most popular and dynamic ski and snowboard...
The Low Anthem Announce Worldwide Headlining Dates For 2011
Fresh off a string of shows with Emmylou Harris that the Hartford Courant called "dazzling," The Low Anthem have confirmed an initial run...
Suwannee Springfest Announces Lineup, Celebrates 15th Year
Big IV Productions is proud to announce details for the 15th annual Suwannee Springfest. The perfect way to kick-off festival season,...
Reverend Peyton's Big Damn Band confirms tour with Reverend Horton Heat
With the release of "The Wages," earlier this year Reverend Peyton and his wife, Washboard Breezy Peyton and Aaron "Cuz" Persinger on ...
Bobby Long Brings A Winter Tale To Your Town | Announces 2011 Tour Dates
British singer-songwriter Bobby Long will begin 2011 by embarking on the first leg of a North American concert tour as a headliner in...
New Frank Zappa Release, Hammersmith Odeon
Early in 1978 Frank Zappa played London's Hammersmith Odeon and these concerts provided the source for the Basic Tracks for 1979's Sheik YerBouti. Hammersmith...
THE BRIDGE Announce New Album 'National Bohemian' and 2011 Tour Dates
The Bridge will release their fifth studio album National Bohemian on February 1, 2011 through Woodberry Records/Thirty Tigers. For its latest effort, the Baltimore-based...


text:
<?php

namespace AppBundle\Controller;

use AppBundle\Entity\Adventure;
use AppBundle\Entity\ChangeRequest;
use AppBundle\Entity\Review;
use AppBundle\Entity\User;
use AppBundle\Form\Type\ChangePasswordType;
use Doctrine\ORM\Query\Expr;
use Sensio\Bundle\FrameworkExtraBundle\Configuration\Method;
use Sensio\Bundle\FrameworkExtraBundle\Configuration\Security;
use Symfony\Bundle\FrameworkBundle\Controller\Controller;
use Sensio\Bundle\FrameworkExtraBundle\Configuration\Route;
use Symfony\Component\HttpFoundation\Request;
use Symfony\Component\HttpFoundation\Response;
use Symfony\Component\Security\Core\User\UserInterface;

/**
 * @Route("/profile")
 * @Security("is_granted('IS_AUTHENTICATED_REMEMBERED')")
 */
class ProfileController extends Controller
{
    /**
     * @Route("/", name="profile")
     * @Method("GET")
     *
     * @return Response
     */
    public function overviewAction(UserInterface $user)
    {
        $em = $this->getDoctrine()->getManager();
        $adventureRepository = $em->getRepository(Adventure::class);
        $changeRequestRepository = $em->getRepository(ChangeRequest::class);
        $reviewRepository = $em->getRepository(Review::class);

        $qb = $adventureRepository->createQueryBuilder('a');
        // Get all adventures created by the current user as well as corresponding pending change requests.
        // Sort them by adventures having a change request, then by title
        $adventures = $qb
            ->where($qb->expr()->eq('a.createdBy', ':username'))
            ->leftJoin('a.changeRequests', 'c', Expr\Join::WITH, 'c.resolved = false')
            ->addSelect('c')
            ->orderBy('c.id', 'DESC')
            ->addOrderBy('a.title', 'ASC')
            ->setParameter('username', $user->getUsername())
            ->getQuery()
            ->execute();

        $changeRequests = $changeRequestRepository->findBy([
            'createdBy' => $user->getUsername(),
        ], ['createdAt' => 'DESC', 'resolved' => 'ASC']);

        $reviews = $reviewRepository->findBy([
            'createdBy' => $user->getUsername(),
        ], ['createdAt' => 'DESC']);

        return $this->render('profile/overview.html.twig', [
            'changeRequests' => $changeRequests,
            'adventures' => $adventures,
            'reviews' => $reviews,
        ]);
    }

    /**
     * @Route("/change-password", name="change_password")
     * @Method({"GET", "POST"})
     *
     * @return Response
     */
    public function changePasswordAction(Request $request)
    {
        /** @var User $user */
        $user = $this->getUser();
        $form = $this->createForm(ChangePasswordType::class, $user);
        $form->handleRequest($request);
        if ($form->isSubmitted() && $form->isValid()) {
            // We need to set the password to null to trigger the lifecycle hooks to encode the new plain password.
            // These are only triggered if a mapped property of the entity changes.
            $user->setPassword(null);

            $em = $this->getDoctrine()->getManager();
            $em->merge($user);
            $em->flush();

            $this->addFlash('success', 'Your password was changed.');

            return $this->redirectToRoute('profile');
        }

        return $this->render('profile/change_password.html.twig', [
            'form' => $form->createView(),
        ]);
    }
}

redpajama_set_name: RedPajamaGithub


text:
James Monroe Matthews
MATTHEWS, James Monroe, Superintendent of the County Farm of McDonough County, Ill., was born in Bethel Township, that county, April 22, 1849. He is a son of Jacob and Abigail (Dunsworth) Matthews, natives of Tennessee. His grandfather. Benjamin Matthews, was also a native of that State. At an early period Grandfather Matthews came to Bethel Township, where he was an extensive landholder. Jacob Matthews, the father, owned and operated a grist-mill at Fandon, in that township, where he died in 1859. James M. Matthews, who is the oldest of a family of four children, lived with his parents until the spring of 1866, after which he worked out until his marriage. He was occupied in farming, running a threshing machine and engine, and making pottery. In April, 1903, he bought a farm of twenty-three and one-half acres in the northeast part of Macomb, which he has since sold. In 1901 Mr. Matthews was appointed Superintendent of the County Farm for one year, after which he was for two years engaged in farming. In March, 1904, he was again appointed to his former position for two years. The County Farm comprises 160 acres of land, and contains a substantial brick building of ninety-two rooms.
On May 21, 1872. Mr. Matthews was married to Joanna Shutes Boyd, who was born in Colchester Township, McDonough County, in 1851, and in girlhood attended the public schools. One child, Howard, born in October, 1873, is the offspring of this union. Politically, Mr. Matthews is a Democrat, religiously, belongs to the Christian Church, and fraternally, is affiliated with the I. O. O. F. and the M. W. A.
Source: The Historical Encyclopedia of Illinois and History of McDonough County, compiled by Dr. Newton Bateman, and Paul Shelby, 1907, volume 2, page 946, extracted 12 Sep 2019 by Norma Hass.


Who would vote for them?
The election of 2015 produced what many consider a shock result – a Conservative majority. Social media has been vitriolic… Read more Who would vote for them?
Why use KnitR for scientific publishing?
All the figures and text for this post were created in a KnitR document, as an example of how easy… Read more Why use KnitR for scientific publishing?


You Are Here: Home → What Are 4 Things That People Should Know about Furnaces?
Nobody enjoys being cold, especially not within their own house. After all, the home is a place where people often seek comfort. With a furnace inside the house, most people won't have to worry about wearing dozens of extra layers every day. People will be able to be comfortable inside their home, which means being able to wear what they want and being able to sleep well. Having a furnace inside the house can often be one of the best ways to heat up the entire house.
Attempting to keep warm with other methods aside from having a central heating system is never a good idea. It often results in spending more time, effort, and money than a simple furnace installation would cost. For example, having to buy and wash countless clothes that are worn in layers is tedious. Space heaters cost money and can quickly turn into both a fire hazard and a waste of money. Having a furnace inside the house can be an efficient way to keep everyone comfortable without wasting time, energy, or money on other methods.
Whether a person is installing a completely new heating system inside their house or that person is simply replacing an old and outdated heating system, it is important to take efficiency into account. Replacing an outdated or an ill-functioning heating system with a new furnace will drastically increase the efficiency of that heating system. This can result in a quicker response time when you need the house to be warmer, a quieter startup, more even heating, and an overall increase in efficiency. More often than not, this increase in efficiency will also end up causing energy bills to drop as it won't take as much energy to warm up the house up when there is a new, efficient furnace in the house.
Staying in cold temperatures for a prolonged period of time has been proven to cause health problems. From causing dry skin to exacerbating respiratory problems, cold and dry air is not good for anyone. Not having an efficient or working heating system in the house can lead to an increase in these problems, as there isn't a central heating system that works well enough to warm the house properly. With a new furnace installation Oshawa, everyone inside the house will not only be more comfortable, but they will also be healthier, as they will not be breathing cold, dry air.


Find and save ideas about industrial kitchen island on see more design nyc warehouse, view this item and discover similar industrial work tables for sale at rustic country workbench or kitchen island table top with wonderful patina. Find great deals on for workbench kitchen island shop with confidence.
You searched for kitchen island etsy is the home to thousands of handmade vintage and one a kind products gifts your search no matter what. Find vidos ideas reviews for industrial kitchen work bench right plan your next woodworking project. View this item and discover similar industrial work tables for sale at rustic country workbench top with french base can be used as. Find kitchen island industrial trolley catskill mid sized drawer interior designers wooden with castors, rimforsa work bench offers a practical kitchen island made from steel and bamboo highly durable renewable material that grows naturally strong, diy kitchen islands to really maximize your space found at the flea market and transform it into a island workbench gets new life as, antique industrial wooden kitchen island workbench the steel top has been sealed with coats and entire cleaned sanitized is ready for use.
The work triangle vs zones kingswood designs fy kitchen area fx about remodel stylish home design style biggest bath trends for professional, how to make an awkward space work for you kitchen with dining room designs excellent photo. Small office space furniture ideas kitchen styles imposing work area intended design tiny island for the smart modern pertaining help top tips.


Ah, you've reached another milestone in your playing. Don't you just love when something new clicks? Some "ah-ha" moments take longer than others, but man it never gets old. Congrats!
The thing is, they are music.
Knowing how to play music is a different beast from just playing the guitar.
Can you explain that a little? Going up and down a scale is music to you?
Rodders wrote: AP guitar tuner has changed and doesn't seem to have all the alternative tunings anymore.
I lost the original when my pc crashed and now this new one doesn't seem to be as good.
Can anyone send me the original one ?
That's the thing, i have a little tuner that attaches to the guitar, but it uses those little tiny batteries. If it ever dies on me, it's good to know I won't have to play out of tune. Or if you're traveling, that's one less thing to carry. Something to keep in mind I guess.
Haha, I'm digging the responses.
I actually thought people would appreciate this device. Guess not. I myself have never made my own picks, but i thought this would be a good way to experiment with whatever you have around the house, and do it quickly. To each his own.