CERN Accelerating science

Pulse structure alternatives. Option A+ is the baseline design, with minimal powering requirements for the superconducting RF cavities.

Detailed schematic of the nominal ESS$\nu$SB pulsing scheme, Option A+ from Fig.~\ref{fig:pulse_struct_options}.

Two front-end layouts for a merged proton/H$^-$ beamline. The left-hand layout uses a common LEBT and RFQ, while the right-hand layout merges the two species in the MEBT.

Two layouts for merging the proton/H$^-$ sources. The left-hand layout requires moving the current proton source and bending both beams at 30$^\circ$, the right-hand side layout leaves the proton source unchanged and bends the H$-$ beam by 60$^\circ$.

Schematic cross section of a Penning ion source, from \cite{Faircloth_2018}.

General schematic of an internal RF negative ion source (left) and a cross section of the SNS RF ion source (right), both from \cite{Faircloth_2018}.

General schematic of an internal RF negative ion source (left) and a cross section of the SNS RF ion source (right), both from \cite{Faircloth_2018}.

Beam envelopes for different ion species at different stages in the linac.

Standard proton MEBT, simulations of envelopes (top) and emittance growth for both the MEBT and first DTL tank (bottom), from~\cite{Miyamoto:2014_ess_mebt}.

Standard proton MEBT, simulations of envelopes (top) and emittance growth for both the MEBT and first DTL tank (bottom), from~\cite{Miyamoto:2014_ess_mebt}.

Detailed Schematic for the 45-degree merge-in-MEBT option.

MEBT lattice including the translation stage, indicating the quadrupoles and buncher cavities.

Emittance in the MEBT and the first DTL tank for a nominal H$^-$ beam.

Emittance in the MEBT and the first DTL tank for a nominal H$^-$ beam.

Chopper at full deflection; H$^-$ beam deflected to the intended beam dump.

Layout of the L2R transfer line \cite{JohanssonDrawing}. Sections are colour-coded according to the presence of horizontal and/or vertical bending

Layout of the L2R transfer line \cite{JohanssonDrawing}. Sections are colour-coded according to the presence of horizontal and/or vertical bending

Quadrupole (Q), horizontally bending dipole (H) and vertically bending dipole (V) distributions within 8.52\,m lattice cells for (a)--(c) sections listed in the legend of Fig.~\ref{fig:L2R}.

Assignment of lattice cells according to the presence of horizontal and/or vertical bending; the colour key follows the legend in Fig.~\ref{fig:L2R}. : Section start and end locations, as defined in Fig.~\ref{fig:L2R}, for the proposed lattice, measured from the start of the L2R line.

Transverse $x$ (red) and $y$ (blue) phase advance per cell along the linac and L2R line. Positions are given relative to the start of the DTL. The lattice sections are indicated along the top of the plot.

Intra-beam stripping power loss along the linac and L2R line. Positions are given relative to the start of the DTL. The lattice sections are indicated along the top of the plot.

Energy spread (1\,$\sigma$) along the linac and L2R line, with four cavities operated at the zero-crossing near the end of the L2R line. Positions are given relative to the start of the DTL. The lattice sections are indicated along the top of the plot.

Average transverse beam sizes (left) and emittances (right) for the H$^-$ beam through the length of the linac and L2R transfer line.

Average transverse beam sizes (left) and emittances (right) for the H$^-$ beam through the length of the linac and L2R transfer line.

Temperature dependence of blackbody-radiation stripping for 60\,mA beams at a 4\% duty cycle for the ESS$nu$SB beam energy of 2.5\,GeV, with curves for a more restrictive 8\,GeV case shown as reference. Left and right-hand markers in the legend correspond to fractional loss rate and beam power loss scaled by the left and right-hand $y$ axes, respectively. Reproduced from~\cite{folsom:2021_hmin_strp}.

Intra-beam stripping (IBSt) power losses for a nominal trajectory and a corresponding error study for the ESS$\nu$SB linac (H$^-$ only). Static and dynamic machine errors are incorporated along with beam misalignment. Standard deviations are from the cumulative trajectories of 100 trials.

Power deposition of H$^0$ into beam-pipe and machine element walls for a 62.5{\thinspace}mA H$^-$ beam accelerating to 2.5\,GeV for the ESS$\nu$SB linac. Only IBSt is accounted for.

Traversal of H$^0$ particles from the point of IBSt to collision with the nearest machine-element wall or aperture for the ESS$\nu$SB linac. Inset shows the depositions occurring within 2\,m of stripping.

Dependence of blackbody, IBSt, and Lorentz stripping (quadrupoles only) on average transverse beam size $\sigma_\perp$ for a 2.5\,GeV, 62.5\,mA beam traversing toy FODO lattices (6${\thinspace}$m~$\times$~20 cells) of one quadrupole pair and one bunching gap per cell. Beam parameters are determined by setting phase advance and solving for optimum inputs. A range of 1--90$^\circ$ phase advance runs gives the shown range of beam sizes. Blackbody stripping is simulated separately, assuming a constant $\sigma_\perp$ for each point.

Dependence of IBSt and Lorentz stripping (quadrupoles only) on field gradient for the same lattice and optimisation scheme as Fig.~\ref{fig:lor_v_ibs}.

Simulation results for pulsing Option A+ from Fig.~\ref{fig:pulse_struct_options} ; Top: modulator output voltage and capacitor bank charging waveforms, Bottom: flat top ripple, confirmed to be within acceptable limits.

Simulation results for pulsing Option A+ from Fig.~\ref{fig:pulse_struct_options} ; Top: modulator output voltage and capacitor bank charging waveforms, Bottom: flat top ripple, confirmed to be within acceptable limits.

Power curves for SN18K010 Canon klystron. Curve 4 and 5 have been obtained by introducing a mismatch at the klystron output. This case will not be considered in the following calculations, so the klystron output power is considered at these voltage levels is slightly lower.

Peak power profiles for the superconducting linac at different stages in the RF chain. Blue -- power to cavity; magenta -- klystron output power; orange -- klystron saturated power; grey -- power provided from the modulator to klystrons; cyan -- modulator input power.

Clockwise from top left: Electron beam trajectory simulation in a klystrons, efficiency vs. input power, klystron bandwidth, operation on a mismatched load, efficiency and output power vs. cathode voltage, and efficiency vs. input power at different cathode voltages.

Clockwise from top left: Electron beam trajectory simulation in a klystrons, efficiency vs. input power, klystron bandwidth, operation on a mismatched load, efficiency and output power vs. cathode voltage, and efficiency vs. input power at different cathode voltages.

Saturated output power (top) and efficiency at saturation (bottom) of the HEK-ESS-8 klystrons.

Saturated output power (top) and efficiency at saturation (bottom) of the HEK-ESS-8 klystrons.

Blue -- power to cavity; magenta -- klystron output power; orange -- klystron saturated power; grey -- power provided from the modulator to klystrons; cyan -- modulator input power.

Peak power from modulator to klystrons in the elliptical part of the linac. Blue -- ESS baseline linac; red -- HEK ESS-8 klystrons.

Klystron efficiency along the elliptical linac. Blue -- ESS baseline linac; red -- HEK ESS-8 klystrons.

A swap procedure considered for each cryomodule during an ESS neutron program shutdown period (8--9 weeks each).

A visual outline for scheduling the CM coupler upgrades during the ESS neutron production program and its shutdown periods. This plan takes as few high-risk activities as possible, but remains within the ESS$\nu$SB upgrade timeline.

The first suggested timeline for the installations, aimed at mitigating the operational challenges arising from the required linac upgrade.

The accumulator ring layout.

: Optical $\beta$-functions and the horizontal dispersion $D_x$ in one FODO cell.

: Optical $\beta$-functions throughout the ring.

The permanent orbit bump (upper), to facilitate injection, formed by four dipole magnets marked as red boxes in the lower frame. Four fast kicker magnets in each plane are used to generate an orbit bump additional to the permanent one.

Example of a 10\,mm orbit bump generated by the injection kicker magnets illustrated in Fig.~\ref{fig:injection_bump_magnets}.

The closed-orbit bump amplitude as a function of time during the injection. Six different functions are shown, ranging from a linear slope to a more dramatic exponential slope.

The particle density distribution in horizontal (top row) and vertical (bottom row) phase space resulting from anti-correlated painting with three selected cases of the orbit bump functions, shown in Fig.~\ref{fig:ring:orbit_bumps}. The distribution goes from under-painted (case \#1, left), where the particle density is very high in the centre, to over-painted (right, case \#6), with a underpopulated core. The best case (middle, case \#4) gives the most uniform beam distributions.

The particle distribution (left) and the particle density distribution (right) when correlated painting is used.

The particle density distribution in horizontal phase space (left), vertical phase space (middle) and real space (right) resulting from anti-correlated painting with the orbit bump function in case \#4, see Fig.~\ref{fig:ring:orbit_bumps}.

Transverse beam emittance $\epsilon_T$ with and without space charge (left) and the corresponding tune diagram (right). The plot to the left shows the fraction of the beam that is contained within a specific beam emittance. When space charge is considered, the 100\% beam emittance is roughly 70$\pi$\,mm\,mrad and the tune spread is less than 0.05.

Particle density distribution in the stripper foil using matched injection (left) and mismatched injection (right).

Peak foil temperature as a function of time following several injected pulses. With mismatched injection and four sequential stripper foils the peak temperature stays below 2000\,K.

: RF waveforms of a dual-harmonic cavity and a barrier RF cavity with a single sinusoidal pulse with a frequency 9 times the first harmonic, i.e the revolution frequency.

: The beam energy distribution before accumulation.

The longitudinal particle distribution at the end of injection. If the incoming energy spread is large, i.e. the case of having no cavities in the transfer line (see Fig.~\ref{fig:accumulator:initial_energy_distribution}), it takes a barrier RF cavity with a voltage of 20\,kV to preserve the extraction gap, the border of which is marked with the vertical dotted lines. With a reduced incoming spread, 5-10\,kV are enough.

Optical beta functions $\beta_x$ and $\beta_y$ and horizontal dispersion $D_x$ in one lattice super-period. The blue line at the top marks the location of the primary collimator.

: RMS scattering angle and energy loss for 2.5\,GeV protons interacting with different materials, each having a thickness of 10\,g/cm$^2$.

: RMS scattering angle and energy loss for 2.5\,GeV protons interacting with different thicknesses of tantalum.

Particle loss rate in collimation sections with different collimator types.

Beam-loss map for the accumulator ring for Option~3 (all rectangular-type collimators).

Relationship between collimation efficiency and ring acceptance.

Collimation efficiency and the power loss before reaching secondary collimators as a function of the primary-collimator thickness.

Schematic of the extraction system.

Schematic view of the Lambertson septum magnet~\cite{Rank:2005:1591644}: The beam encounters no magnetic field while injection is ongoing. Once the injection is complete, the kicker magnets are powered and steer the beam towards the other side of the septum blade, where the magnetic dipole field deflects the beam horizontally.

Beam envelopes in the extraction region.

Illustration of the extraction kicker ramping.

SNS injection section, shown schematically, where F1 is the stripper foil; F2 is a second, thick stripper foil to fully strip $H^-$ and $H^0$ to protons; IDSM is the Injection Dump Septum Magnet; and Q is a defocusing quadrupole. From: \cite{Wang:2008zzk}.

Distribution of energy deposition in the copper beam dump.

Distribution of energy deposition in the copper beam dump.

Schematic layout of the injection beam dump with shielding.

: 2D projection.

: 1D projection.

Overview drawing showing the location of the accumulator and the target station, connected by the R2S beam line \cite{Johansson:2020ESS}.

Horizontal and vertical plots of the R2S from \cite{Johansson:2020ESS} and slopes of the neutrino direction. To simplify the simulations, the extraction of the beam at the exit of the septum has the coordinates $x, y, z$ (0; 0; 0).

Transverse phase space of the particles used in the design of the R2S transfer line (240500 macroparticles).

Horizontal (left) and vertical (right) synoptics of the R2S beam line.

Coincidence of the end of the R2S beam line, designed with TraceWin, and the neutrino beam direction in the horizontal (left) and vertical (right) planes.

RMS transverse beam envelopes along the R2S beam line.

Face view of the target station layout. The four targets are named T1, T2, T3 and T4.

Schematic layout of the beam switchyard. D1 and D2 are dipoles that bend the beam in the horizontal plane. D3, D4, D5, and D6 bend the beam in the vertical plane.

Time structure of the incoming beam in relation to the dipoles of the BSY.

RMS transverse beam envelopes and dispersion along the T1 branch of the BSY.

RMS transverse beam envelopes and dispersion along the T2 branch of the BSY.

RMS transverse beam envelopes and dispersion along the T3 branch of the BSY.

\small RMS transverse beam envelopes and dispersion along the T4 branch of the BSY.

Horizontal (left) and vertical (right) synoptics of the BSY.

Overall 3D views of the BSY: top, side (middle), and isometric (bottom) projections. Possible locations for adding diagnostics capable of measuring several characteristics of the beam (i.e., size, position, energy, etc.) are identified with boxes.

Section plane of the collimators.

Time structure of kickers for the BSY.

RMS transverse beam envelopes and dispersion along the T3 branch of the BSY when two quadrupoles, Q34 and Q37, are not functioning (failure scenario).

Overview of the target station facility.

: The four-horn system.

: Transverse view of one horn.

: Evolution of the horn profile.

: Genetic algorithm convergence throughout the iterative process.

Definition of the horn parameters and their values obtained after optimisation.

: Positive polarity

: Negative polarity

3D model of the target concept based on a packed bed of titanium spheres.

Map of power deposition inside a titanium granular target.

: Helium flow parameters obtained from the analytical approach for transverse flow (first sector).

: $(T_s)_{max}$, $(T_s)_{min}$ and $\Delta T_s$ of spheres in each beam cycle (first sector).

Distribution of superficial velocity [\SI[per-mode=symbol]{}{\meter \per \second}] (a), temperature [\SI{}{\kelvin}] (b), absolute pressure [\SI{}{\pascal}] (c), and density [\SI[per-mode=symbol]{}{\kilogram \per \meter \cubed}] (d) of helium flowing upwards in the transverse direction through the first two sectors of the target under constant helium mass flow \SI[per-mode=symbol]{300}{\gram\per\second} and with the non-homogeneous power deposition inside the target having a total value of $\dot{Q} = $\SI{138.53}{\kilo\watt}

: For a sphere with radius \SI{1.5}{\milli \meter}.

: For a sphere with radius \SI{0.75}{\milli \meter}.

Sketch of the magnetic horn proposed for ESS$\nu$SB.

Magnetic flux density in tesla inside a horn and surrounding space, at time \SI{50}{\micro \second} when the value of current is equal to \SI{350}{\kilo \ampere} (after the current discharge).

Power density in \SI[per-mode=symbol]{}{\kilo \watt \per \centi \meter \cubed} inside the magnetic horn skin due to secondary particles.

Joule power density per unit volume in \SI[per-mode=symbol]{}{\watt \per \meter \cubed} in the horn skin, at time \SI{50}{\micro \second} (horn outer skin is not shown).

Model of the horn with values for each section of power deposition, required mass flow rate, and temperature.

: Maximum stress levels in the horn skin due to magnetic forces (at $t = \SI{90}{\micro \second}$).

: Maximum longitudinal displacement from magnetic forces (at $t = \SI{64}{\milli \second}$).

Thermal stress in a magnetic horn, assuming heat transfer coefficient between horn and water h = \SI[per-mode=symbol]{3000}{\watt \per \meter \squared \per \kelvin}.

: Direction of helium inflow and outflow.

: Cross-section of the proposed horn-target integration (horn in purple, target container, target shell and connecting plates in red, thermal isolation in blue) used for the calculations.

Pattern of helium entry and exit openings of uniform size in the target container.

: Helium temperature.

: Helium pressure.

: Helium density.

: Helium velocity streamlines.

: Temperature in the outer shell