Figure 1

Proposed PAMELA layout.Reuse & Permissions

Figure 2

Layout of the proton lattice with injection orbit (inner dotted line) and maximum energy orbit (outer dotted line).Reuse & Permissions

Figure 3

Regions of stable optics for proton lattice. The second stability region of the solution of Hill’s equation is shown in black filled points.Reuse & Permissions

Figure 4

Beta functions in one cell of proton lattice.Reuse & Permissions

Figure 5

Cell tunes for the proton ring throughout acceleration for the case of rectangular shaped magnets using a polynomial fit to the ideal field profile. The three magnets are aligned parallel with each other. Horizontal cell tune in (a) and vertical cell tune in (b). Dashed lines and associated numbers show total tune of a 12 cell ring.Reuse & Permissions

Figure 6

Change in closed orbit position through acceleration, tracked using ZGOUBI.Reuse & Permissions

Figure 7

Orbit distortion as a result of introducing horizontal and vertical alignment errors to the proton ring. The black points correspond to the mean of the ten runs at each $\sigma$ value and error bars correspond to the rms spread of the ten runs. The shaded region is the area between the maximum and minimum linear fit, where the central linear fit determines the amplification factor in each case. (a) Fitted distribution of horizontal alignment errors. (b) Fitted distribution of vertical alignment errors.Reuse & Permissions

Figure 8

Dynamic aperture vs (left) horizontal cell tune (${\nu }_x$), (right) vertical cell tune (${\nu }_y$). The optimized lattice of rectangular shaped magnets with polynomial fit to strength is used.Reuse & Permissions

Figure 9

Stable working points for the 9.3 m carbon lattice design with a packing factor of 0.65. The second stable region is shown in black filled points.Reuse & Permissions

Figure 10

Beta functions in one cell of the carbon lattice as calculated with S-Code.Reuse & Permissions

Figure 11

Variation of horizontal cell tune (a) and vertical cell tune (b) for different orders of multipoles for the carbon ring. Dotted lines correspond to integer and half-integer resonances of the total machine tune.Reuse & Permissions

Figure 12

Variation of orbit position in the horizontal direction during acceleration.Reuse & Permissions

Figure 13

Dynamic aperture vs (left) horizontal cell tune (${\nu }_x$), (right) vertical cell tune (${\nu }_y$).Reuse & Permissions

Figure 14

Layout of the matched transfer line for ${\mathrm{C}}^{6+}$ ions from the proton to the carbon ring. Vertical bends are shown with dashed lines, yellow magnets bend in the vertical plane, orange dipoles bend in the horizontal plane, red rectangles are focusing quadrupoles (in the horizontal plane), and blue rectangles are defocusing.Reuse & Permissions

Figure 15

The carbon lattice.Reuse & Permissions

Figure 16

Typical particle traces through the PAMELA triplet; the F and D magnets are indicated schematically by the red and green boxes, and the blue arrow shows the direction in which the D magnet must be displaced for the offset solution.Reuse & Permissions

Figure 17

A typical magnetic field using the scaling law in black, with the red curve highlighting the part experienced by the particles.Reuse & Permissions

Figure 18

Vertical magnetic field of the carbon F magnet, comparing the ideal scaling law with the real magnetic field. For tune stabilization (see text) the quadrupole component was increased by 4.5% and the sextupole component by 2%. The octupole and decapole components were decreased by 4% and 25%, respectively.Reuse & Permissions

Figure 19

The local $k$ value with and without decapole field component.Reuse & Permissions

Figure 20

Peak magnetic field on the wire of the D magnet for the carbon ring for the 4th layer from the center.Reuse & Permissions

Figure 21

Load line of the carbon F/D magnet.Reuse & Permissions

Figure 22

(a) Equivalent circuit of dual-gap cavity and associated tetrode power amplifier (PA), with core biasing current input and (b) schematic of cavity design.Reuse & Permissions

Figure 23

Side view of planned ferrite-loaded rf cavity.Reuse & Permissions

Figure 24

Material properties of NiZn ferrite 4E2. (a) Frequency dependence of complex permeability. (b) Temperature dependence of imaginary part of permeability. (c) The magnetic flux density B as a function of the magnetic field strength H.Reuse & Permissions

Figure 25

Frequency dependence of cavity gap voltage.Reuse & Permissions

Figure 26

Frequency dependence of cavity gap current.Reuse & Permissions

Figure 27

Frequency dependence of cavity power consumption.Reuse & Permissions

Figure 28

Measured frequency dependence of $Q$ value of 4E2 under biased condition.Reuse & Permissions

Figure 29

The beam injection scheme.Reuse & Permissions

Figure 30

Longitudinal velocities of ${\mathrm{C}}^{6+}$ (top), ${\mathrm{C}}^{5+}$ (middle), and ${\mathrm{C}}^{4+}$ (bottom) ions, immediately after the ECRIS. ${\mathrm{C}}^{6+}$ shows the highest kinetic energy applying the same extracting voltage, here 24 kV, to all species.Reuse & Permissions

Figure 31

MEBT injection layout for PAMELA, based on a cyclotron inside the FFAG ring.Reuse & Permissions

Figure 32

Beta functions and dispersion for the proton line shown in Fig. 31. The optics is shown in the inverse configuration, which means that the cyclotron is located on the right and the FFAG cells are located on the left.Reuse & Permissions

Figure 33

Horizontal and vertical betatron functions in the carbon line obtained via MAD-X (again in the inverse configuration).Reuse & Permissions

Figure 34

Phase space motion for vertical extraction.Reuse & Permissions

Figure 35

(a) 3D kicker model in Opera and (b) integrated horizontal and vertical magnetic field in the kicker.Reuse & Permissions

Figure 36

(a) Double-bridged T-network and (b) traveling wave kicker. For the double-bridged T-network the required capacitance $C$ can be calculated from the kicker inductance and the termination resistance $R$: $C=L_{\mathrm{mag}}/(2R_{\mathrm{term}}^2)$. The required inductance can be calculated from $L=L_{\mathrm{mag}}/4$.Reuse & Permissions

Figure 37

Schematic of the PFN for (a) protons and (b) carbon. The thyratrons have been selected after extensive discussions with e2V. The kicker magnet is shown schematically as a resistance and inductance.Reuse & Permissions

Figure 38

Pulse shapes of the (a) proton and (b) carbon kicker.Reuse & Permissions

Figure 39

A complete PFN assembly for a kicker for the proton ring; the box houses two PFNs.Reuse & Permissions

Figure 40

PFN test circuit, courtesy of Johan Fopma (Oxford).Reuse & Permissions

Figure 41

PFN test circuit—voltage across magnet.Reuse & Permissions

Figure 42

Front views of the extraction septum for the carbon ring (a) whole septum (b) detail.Reuse & Permissions

Figure 43

Current density in the bedstead coils as a function of the horizontal position. Shown are the theoretically required current density for a 2D case and the final current density in the model, which takes into account the different lengths of the bedstead magnets and nonlinearities of the iron yoke.Reuse & Permissions

Figure 44

Horizontal magnetic field in the septum as a function of the horizontal position. The real magnetic field is averaged over various vertical positions within the septum bore.Reuse & Permissions

Figure 45

Integrated horizontal (a) and vertical (b) magnetic field in the septum bore as a function of the position.Reuse & Permissions

Figure 46

Load line of the FFAG septum.Reuse & Permissions

Figure 47

Vertical stray field experienced by the circulating particles. The septum is shown from underneath, the light blue area indicates the part which is covered by the iron yoke.Reuse & Permissions

Figure 48

Stray horizontal magnetic field at a vertical position of $-43\mathrm{mm}$. The field is shown for a horizontal position from $-100$ to 100 mm in 40 mm steps [56].Reuse & Permissions

Figure 49

Phase space ellipses of four emittances that result in smears of 0.1, 0.25, 0.5, and 1. The black dots represent the particles at the start of the lattice while the grey dots represent the same particles at the end. Increasingly large initial emittances are used simply for clarity in the figure.Reuse & Permissions

Figure 50

The acceptances for 30 m of transport line using cells with nonscaling magnets in a DFFD configuration. The size of the dots are proportional to the square root of the acceptance. Black dots represent acceptances $>10\mathrm{mm}\mathrm{mrad}$ and grey dots represent lower acceptances. For scale: the largest acceptance (at $k/x_0=5$ and $\mathrm{D}/\mathrm{F}=1.15$) is $101.75\pi \mathrm{mm}\mathrm{mrad}$ and the smallest (at $k/x_0=20$ and $\mathrm{D}/\mathrm{F}=1.3$) is $0.03\pi \mathrm{mm}\mathrm{mrad}$.Reuse & Permissions

Figure 51

The acceptances for 30 m of transport line using cells with nonscaling magnets in a FDDF configuration. See Fig. 50 for description of dot size and color.Reuse & Permissions

Figure 52

The dependence of the dispersion in the center of the long drift of a transport cell on the field index $k/x_0$.Reuse & Permissions

Figure 53

The acceptances for 30 m of transport line using cells with nonscaling magnets in a DFFD configuration, $k/x_0$ close to 12 and $\mathrm{D}/\mathrm{F}$ close to 1.15. For scale, the largest dot at $k/x_0=7.5$ and $\mathrm{D}/\mathrm{F}=1.17$ represents an acceptance of $122.03\pi \mathrm{mm}\mathrm{mrad}$. See Fig. 50 for description of dot size and color.Reuse & Permissions

Figure 54

Equilibrium orbits at 369, 549, and $729\mathrm{MeV}/c$ through cell with $k/x_0=11$ and a DF ratio of 1.17. In ascending order of momentum the orbits are shown as solid, dashed, and dotted lines.Reuse & Permissions

Figure 55

Horizontal (solid) and vertical (dashed) beta functions through cell with $k/x_0=11$ and a DF ratio of 1.17.Reuse & Permissions

Figure 56

Fields along the equilibrium orbits at 369, 549, and $729\mathrm{MeV}/c$ through cell with $k/x_0=11$ and a DF ratio of 1.17. In ascending order of momentum the orbits are shown as solid, dashed, and dotted lines.Reuse & Permissions