Beam Shaping in Laser Powder Bed Fusion: Péclet Number and Dynamic Simulation

Abstract

A uniform distribution of power density (energy flux) in a stationary laser beam leads to a decrease in the overheating of the material in the center of the laser beam spot during laser powder bed fusion and a decrease in material losses due to its thermal ablation and chemical decomposition. The profile of the uniform cylindrical (flat-top) distribution of the laser beam power density was compared to the classical Gaussian mode (TEM₀₀) and inverse Gaussian (donut) distribution (airy distribution of the first harmonic, TEM_01* = TEM₀₁ + TEM₁₀). Calculation of the Péclet number, which is a similarity criterion characterizing the relationship between convective and molecular processes of heat transfer (convection to diffusion) in a material flow in the liquid phase, shows that the cylindrical (flat-top) distribution (TEM_01* + TEM₀₀ mode) is effective in a narrow temperature range. TEM₀₀ shows the most effective result for a wide range of temperatures, and TEM_01* is an intermediate in which evaporation losses decrease by more than 2.5 times, and it increases the absolute laser bandwidth when the relative bandwidth decreases by 24%.

1. Introduction

The well-known drawback of some laser material-processing technologies is non-uniform thermal conditions in the spot. The material is overheated in the center of the laser spot when an excess of the energy leads to intensive material evaporations and chemical decompositions [1,2,3,4], which is not characteristic of other additive technologies using alternative sources of concentrated energy flow [5,6]. Inversely, the material does not attain the necessary processing temperature at the periphery of the spot, and the energy is essentially lost by heat diffusion in the treated body (the target) [7,8,9]. Modern optics proposes shaping a laser beam that provides alternative laser power density distributions of transverse electromagnetic (TEM) mode:

• Airy distribution of the first harmonic (donut) TEM_01* = TEM₀₁ + TEM₁₀;
• Uniform cylindrical (flat-top) distribution TEM_FT = TEM_01* + TEM₀₀.

These technical solutions have multiple laser powder bed fusion attempts but have never been researched theoretically with correction to the beam motion [10,11,12].

The lack of a reliable solution in terms of heat redistribution leads to the following disadvantages affecting the quality of parts obtained by laser-additive manufacturing and processing productivity (Figure 1) [13,14,15,16,17]:

-

Local overheating, capturing the underlying layers, creating additional stresses during metal solidification (partially solved by subsequent heat treatment and preliminary heating of the substrate) [18,19,20];

-

Active evaporation of the material and its chemical interaction with the atmosphere of the chamber (reduced due to the use of more gentle processing modes, which dramatically affects productivity) [21,22,23];

-

Ejecting material from the processing area (reduces the surface quality of the part itself, damages the optics, and is reduced by gentle modes and preheating of the platform) [24,25,26].

An obvious disadvantage of using optical means for redistributing laser energy into the beam can be its expansion by 150–350%, which may not allow for obtaining more precision parts, but can become a significant advantage in the production of products with dimensions of more than 100 mm, for which the width of the heat-affected zone will be significantly reduced [27,28]. Figure 1 is based on the results of optical diagnostics and video monitoring described in detail in [27].

There are many factors that influence the final surface quality (roughness, uniformity, and dimensional accuracy) [29,30,31,32,33] such as:

• laser power, spot size, and laser power distribution among the laser system and optic parameters,
• scanning speed and strategy and hatch distance among strategy parameters,
• powder particle size, shape and morphology, and layer thickness among powder parameters,
• inertness of the atmosphere, impermeability of the chamber, dimensions of the part on the working platform (maximum angle of deviation of the beam from the vertical), and so on.

The conventional power (energy flux q, W/mm²) density distribution in radius r of the laser focus is the classical bell-like one approximated by the normal Gauss distribution (Laguerre–Gaussian mode, circularly symmetric beam profile TEM₀₀) of the optical resonator as:

$$q=\frac{P}{\mathsf{\pi }{r}_0^2}\exp \left(-\frac{r^2}{r_0^2}\right),$$

(1)

where P is the laser beam power, W and r₀ is the radius circle, mm.

In some laser-based technologies such as lithography (photo-activated processes) [34,35], laser scribing [36,37], and thin surface laser treatment (including medical purposes) [38,39,40,41], the optimal beam profile seems to be the flat-top (TEM_FT) one that provides the energy flux’s uniformity (uniform laser power density distribution). The typical powder consolidation mechanisms in laser powder bed fusion are thermo-activated [42]. Then the objective is transferred from the uniform power density distribution (energy flux q, W/mm²) to a radiation-induced uniform temperature field T (°C).

Since the thermal energy is released on an adiabatic plane bounding a uniform conducting half-space inside a circle of radius r₀ (mm), with radial distribution [43]:

$$q=\frac{P}{2\mathsf{\pi }{r}_0^2}\frac{1}{\sqrt{1-r^2/r_0^2}},$$

(2)

the temperature rise over the circle:

$$T_0=\frac{P}{4\lambda r_0},$$

(3)

where λ is the material thermal conductivity, W/mm·K. In this case, the laser radiation is absorbed by layered powder to heat a massive body with conduction as the principal heat transfer mechanism. Then profile (2) can be better for laser powder bed fusion and similar laser-based powder technologies. TEM_FT profile (the cylindrical flat-top temperature distribution) is challenging to obtain because of a discontinuity at the beam boundary where r = r₀. Then the airy distribution of the first harmonic, (donut of the first overtone) TEM_01*, seems to be a reasonable compromise [43]:

$$q=\frac{P}{\mathsf{\pi }{r}_0^2}\frac{r^2}{r_0^2}\exp \left(-\frac{r^2}{r_0^2}\right),$$

(4)

In the thermo-activated processes, the laser beam scans the powder surface, resulting in a non-uniform temperature distribution over the laser spot for various laser beam profiles [44,45]. An inverse problem of heat diffusion for the scanning laser beam can be solved to find the ideal power density distribution. Still, the solution mainly depends on the scanning speed factor—its value and direction. The influence of direction on the absorbed energy flux shows that the laser beam profile would be asymmetric. Moreover, the laser beam scans quite fast (up to 400 mm/s) and changes direction rapidly. Therefore, it can be an even more complicated scientific and technical task never solved before, since most of the published work on beam profiling considers the symmetric beam for their calculations.

This work aims to compare three types of abovementioned laser beam profiles, research the influence of the scanning speed in a linear medium, and develop a non-linear model, including the material evaporation factor.

2. Numerical Simulations

2.1. Simulations and Influence of Scanning Speed

The powder layer on the target surface is considered thermally thin and is not taken into account. Laser radiation is supposed to be absorbed on the surface. In the case of partial reflection, the laser power in the equations mentioned above means the absorbed part of the laser beam radiation. In the coordinate system moving with the scanning speed, the steady-state heat diffusion equation is [43]:

$$\alpha \Delta T+u_s\frac{\partial T}{\partial x}=0,$$

(5)

where u_s is scanning speed, m/s; α is the thermal diffusivity, m²/s; and Δ is the Laplace operator. Equation (5) is solved by numerical or analytical methods where possible, with boundary condition:

$$T\to T_a\mathrm{at}x\to \pm \infty ,y\to \pm \infty ,z\to \infty ,$$

(6)

where T_a is the ambient temperature. The target surface z = 0 is adiabatic, excluding the laser spot where

$$-\lambda \frac{\partial T}{\partial z}=q.$$

(7)

The temperature fields are presented in Figure 2 and Figure 3.

The scanning speed is specified by the thermal Péclet number:

$$\mathrm{Pe}=\frac{2r_0{u}_s}{\alpha }.$$

(8)

The temperature rise relative to the ambience (T − T_a) is normalized by T₀ specified by Equation (3). Normalizing coordinates by r₀ makes the obtained results universal for a linear conductive medium. The results significantly depend on the Péclet number. The top row in Figure 2 shows two-dimensional views of laser profiles (1), (2), and (4) normalized by [43] (Figure 3a,b):

$$q_0=\frac{P}{\mathsf{\pi }{r}_0^2}.$$

(9)

The normalized graphs of profiles are as follows (Figure 3c–e):

$$\frac{q_{{\mathrm{TEM}}_{00}}}{q_0}=e^{\left(-\frac{r^2}{r_0^2}\right)},$$

(10)

$$\frac{q_{{\mathrm{TEM}}_{\mathrm{FT}}}}{q_0}=\frac{1}{2·\sqrt{1-\frac{r^2}{r_0^2}}},$$

(11)

$$\frac{q_{{\mathrm{TEM}}_{01*}}}{q_0}=\frac{r^2}{r_0^2}·e^{\left(-\frac{r^2}{r_0^2}\right)}.$$

(12)

The other rows in Figure 2 are two-dimensional temperature distributions over two characteristic planes. The 3D plot of the implicit function is shown in Figure 3a.

Figure 3f shows all the obtained results as profiles of the surface temperature along line y = 0, z = 0. For all laser profiles, the temperature profiles decrease with the increase of Pe that corresponds to the increase of the scanning speed. The forward temperature front becomes sharper with the increase of Pe, and the backward temperature front is insensible to Pe, according to the well-known asymptotics:

$$\frac{T-T_a}{T_0}=\frac{2}{\mathsf{\pi }}\frac{r_0}{R}\exp \left(\frac{\mathrm{Pe}}{4}\frac{x-R}{r_0}\right),$$

(13)

with R² = x² + y² + z², shown by dashed lines in Figure 3f. In the case of mode TEM₀₀, all three numerically calculated temperature profiles are bell-like. At Pe = 0, the maximum is in the origin. The numerically obtained maximum value is about the analytical result T_max,

$$\frac{T_{\max }-T_a}{T_0}=\frac{2}{\sqrt{\mathsf{\pi }}},$$

(14)

shown by a horizontal dash in Figure 3f. The increase of Pe slightly shifts the position of the temperature maximum in the direction opposite to that of the scanning speed vector that is explained by the thermal inertia of the target.

At Pe = 0, the flat-top laser beam profile forms steady-state temperature distribution

$$\frac{T-T_a}{T_0}=\frac{2}{\mathsf{\pi }}\arcsin \frac{2r_0}{\sqrt{{(r-r_0)}^2+z^2}+\sqrt{{(r+r_0)}^2+z^2}},$$

(15)

where r² = x² + y², with an exactly horizontal plate over the laser spot. When Pe increases, this plate inclines towards the scanning speed vector and slightly sags. In the case of donut mode, the surface temperature distribution inherits the ring-like ridge. The ridge becomes more asymmetric with the increase of Pe (Figure 3f).

2.2. Temperature and Energy Flux Profiles

Temperature distribution in a cross-section perpendicular to the scanning direction cannot objectively characterize the temperature conditions for laser powder bed fusion because retarding the maximum target temperature relative to the central cross-section x = 0. The retardation depends on the scanning speed value and the distance from the scanning axis (X). The most representative quantity is the maximum temperature along axis X for threshold-like and Arrhenius temperature dependencies of the process kinetics. Figure 4a shows the transverse profile of the quantity on the surface [43]:

$$\underset{x}{\max }T(x,y,0),$$

(16)

The asymptotics at Pe = 0 are given by Equation (13) at x = 0. At Pe = 0.71 and Pe = 2.86, the asymptotics are obtained by numerical treatment of Equation (13) by Equation (16). The widths of the re-melted zone on the surface often estimate the contact’s width between the consolidated powder, and the substrate can be deduced by this profile.

The transverse profiles of the surface temperature shown in Figure 4a present the thermal conditions for laser powder bed fusion. They cannot be compared with the tested laser beam profiles because all the obtained temperature profiles have different absolute maxima. The tentative laser-beam radius r₀ is not an objective measure of its width applicable to various beams’ radial profiles. Thus, beam TEM_01* in Figure 4b seems wider than beam TEM₀₀ at the same r₀. Let us estimate the width of a laser profile by its diameter at half-maximum d_½ that is conventional in laser technology applications. The scheme for estimating the corresponding radius at half-maximum r_½ = d_½/2 is shown in Figure 4b and

Table 1. Calculated absolute maximum of temperature T_max versus Péclet’s number Pe.

Laser Beam Profile	Beam Radius at Half Maximum, r1/2/r0	(Tmax − Ta)/T0
		Pe = 0	Pe = 0.71	Pe = 2.86
TEM00 (Gaussian)	$\sqrt{\ln 2}=0.8326$	$2/\sqrt{\mathsf{\pi }}=1.128$	1.027	0.8417
TEM01* (donut)	1.6366	1.6453	0.5889	0.4735
TEMFT (flat-top)	1	1	0.9613	0.8819

.

It should be noted that temperatures above T_max are unallowable because of material evaporation or chemical decomposition. Temperatures below the minimum T_min are not sufficient to complete the specified physical or chemical processes. The boiling point is specified as T_max, and the melting point is T_min for laser powder bed fusion of pure metals [46,47]. For alloys, T_max and T_min are determined by the component with the lowest boiling and melting points, correspondingly.

The temperature dependencies of the kinetic constants can be taken into account to define the laser powder bed fusion interval (T_min, T_max). The maximum temperature in the laser-processing zone and the width of the laser beam characterized by d_1/2 or r_1/2 can be effectively controlled by variation of the laser power or by laser beam expansion. The former quantity can be set at T_max. The latter quantity can be set at the specified dimensional uncertainty.

Figure 5 shows the same temperature profiles as in Figure 4a to apply the chosen criterion for evaluating the laser beam profiles. However, these profiles are renormalized by their absolute maxima, height, laser beam radii at half maximum, and width. The normalizing constants for all the nine testing profiles are obtained from the data shown in Figure 4a,b and Table 1. A qualitative review of the temperature profiles shown in Figure 5 indicates that laser profile TEM_FT results in the broadest top of the temperature profile, as expected. Laser profile TEM₀₀ results in the broadest base of the temperature profile. This means that evaluating the three tested laser profiles is not straightforward and depends on the acceptable temperature range of laser treatment T_max − T_min relative to the maximum temperature increment T_max − T_a. If the acceptable temperature range is narrow, the treated band of the surface is near the top level of the temperature profile. In this case, theoretically, the flat-top profile provides the widest laser-treated band, which means the most effective use of the laser energy. If the acceptable temperature range is wide, the most effective profile seems to be TEM₀₀.

3. Model Evaluation

3.1. Quantitative Evaluation

Let us introduce the width of the laser-treated band B_n where non-dimensional parameter γ for quantitative evaluation of the laser beam profile characterizes the relative temperature range of the laser treatment [43]:

$$\gamma =\frac{T_{\min }-T_{\mathrm{a}}}{T_{\max }-T_{\mathrm{a}}}.$$

(17)

The definitions of B_1/2 and B_0.9 are shown in Figure 5. Band B_1/2 approximately corresponds to laser powder bed fusion of metals and alloys such as CoCr at the ambient temperature T_a with T_max equal to the boiling/decomposition point (~2800–3300 °C) and T_min equal to the melting point (~1250–1650 °C) [48]:

$${\gamma }_{CoCr}=\frac{1458 ℃-20 ℃}{3000 ℃-20 ℃}\approx 0.4826.$$

(18)

The main properties of the cobalt-chromium alloy are shown in

Table 2. Properties of the cobalt-chromium alloy (64–65% of Co, 29–30% of Cr).

Properties	Density, g/cm3	Melting Point, °C	Boiling Point, °C	Tensile Strength, kN/cm2	Yield Strength, kN/cm2	Young’s Modulus, GPa	Coefficient of Thermal Expansion, ×10−6 °C−1	Thermal Conductivity, W/(m·K)
CoCr alloy	8.0–8.4	1250–1650	2800–3000	≥61.7–70	≥50–64	210–250	11.2–14.2	13

. The data presented in the table are taken from [49,50].

Band B_0.9 corresponds to laser-additive manufacturing of oxide ceramics at the ambient temperature T_a with T_max equal to the temperature of chemical decomposition (~2900 °C) [51,52,53,54,55]. T_min should be chosen as high as possible because of the Arrhenius temperature dependence of the powder consolidation rate [56].

The calculated values of B_1/2 and B_0.9 versus Péclet’s number for the laser beam profiles are shown in

Table 3. Calculated widths of the laser-treated band B_1/2 and B_0.9 versus Péclet’s number.

Laser Beam Profile	B1/2/d1/2			B0.9/d1/2
	Pe = 0	Pe = 0.71	Pe = 2.86	Pe = 0	Pe = 0.71	Pe = 2.86
TEM00 (Gaussian)	1.57	1.485	1.32	0.53	0.535	0.50
TEMFT (flat-top)	1.415	1.28	1.118	1.012	0.974	0.775
TEM01* (donut)	1.39	1.24	1.07	0.80	0.70	0.565

and Figure 6. In the considered range of Péclet’s numbers (Pe = 0–2.86), the conventional Gaussian profile of TEM₀₀ seems to be the most effective for the wide temperature range of laser treatment of ½ (alloys, metals) when the flat-top profile can be significantly more advantageous for the narrow temperature range of 0.9 (mostly oxide ceramics). For B_1/2, profile TEM_01* seems to be the least effective one, and the flat-top is intermediate. For B_0.9, profile TEM₀₀ seems to be the least effective one, and TEM_01* is intermediate.

3.2. Dynamic Evaluation

Let us calculate the steady temperature at the laser spot boundary for two laser modes and a laser power of 100 and 400 W. The experimental diameter of the laser spot will be approximately 100 µm (0.001 m) for the TEM₀₀ mode and 300 µm (0.003 m) for the TEM_01* mode (

Table 4. The steady temperature values at the laser spot boundary for two laser modes.

Laser Beam Profiles	Laser Spot Diameter, mm	Steady Temperature (Tmax − Ta), K
		P = 100 W	P = 400 W
TEM00 (Gaussian)	~0.1	1923	7692
TEM01* (donut)	~0.3	641.03	2564

) [57]. As can be seen, with an increase in the power of laser radiation to 400 W, due to excess heat, a multifaceted local overheating is predicted (the calculated temperature is 2.56 times higher than T_max) at the boundary of the laser radiation of the Gaussian mode (as a result, active evaporation of metal from the processing zone). At the same time, when using the reverse Gaussian profile (donut), the temperature at the edge of the laser spot does not reach T_min (less than 2.34 times), which means that there is no sufficient heat to initiate the CoCr alloy granule fusion. The powder consolidation temperature can be closer to the melting temperature. Implicit graphs of the function of temperature on the radius for a cobalt-chromium alloy (λ = 13 W/(m·K)) depending on the power of laser radiation are shown in Figure 7 (Equation (3)). It should be noted that Figure 7a is an implicit graph of the temperature (T_max − T_a) on the radius and laser power function for the material with the mentioned material thermal conductivity, where the solution area is marked red, since only values above zero can be taken into account for technological purposes, since other areas have no physical sense in the context of engineering.

Table 5. Parameters of laser powder bed fusion chosen for modeling.

Factor	Measuring Unit	Values
Absorbed power of the beam, P	W	100	400
Laser beam radius, r0	mm	~0.1/2	~0.3/2
Scanning velocity, us	m/s	0.0213	0.0286
Normalized power density distribution, q0	W/m2	0.320 × 108	0.142 × 108
Specific energy contribution, E	J/m2	1.5 × 105	0.5 × 105
Péclet’s number, Pe	-	0.71	2.86

presents two evaluated groups of laser beam parameters based on the experimental data obtained by optical achievements of the laser beam profiles using an expander and profiler installed in the LPBF setup and optical evaluation of the obtained profiles [28]. Specific energy contribution (J/m²) was calculated by:

$$E=\frac{q_0}{u_s}.$$

(19)

Two numerical calculations for Gaussian (Equation (1)) and donut (Equation (4)) laser beam profiles are made for each group. Thermal diffusivity of CoCr alloy is presented in

Table 6. Thermal diffusivity α of CoCr alloy.

Thermal Diffusivity α, cm2/s
at 20 °C	at 500 °C
0.02–0.14	0.03–0.074

[58,59]:

$$\alpha =\frac{\lambda }{\rho ·C_p},$$

(20)

where ρ is density, kg/m³ and C_p is specific heat capacity, J/(kg·K). The dependence of the Péclet number on the laser spot radius and scanning speed for a cobalt-chromium alloy is shown in Figure 8.

Figure 9 shows the calculated temperature fields for two types of laser beam profiles: TEM₀₀ and TEM_01* at laser powers of 100 and 400 W, correspondingly, when laser beam diameters are 0.109 and 0.310 mm, respectively. The difference from Figure 2 is that laser beam profiles are shown at the level of calculated steady temperatures (Table 4). Formation of the temperature plateau is explained by a small value of overheating sufficient for evaporation under the given conditions. In the case of mode TEM_01*, the characteristic temperature sink is still visible in the center. The energy losses for evaporation are listed in

Table 7. Calculated values of power loss for evaporation P_v for CoCr alloy for the laser beam profiles.

Parameter	Evaporation Loss, Pv (W)
	TEM00, P = 100 W, Pe = 0.71	TEM01*, P = 400 W, Pe = 2.86
Max vapor velocity uv, m/s	3.63	14.51
Max recoil pressure precoil − p0, Pa	17.67	267.67
Mass loss rate Lmass, mg/s	144.30	520.22
Recoil force Frecoil, mN	0.55	7.57
Power loss for evaporation Pe, W	3.53	2.68

. The corresponding mass losses are proportional to the energy ones [43]. Comparison of values listed in Table 7 indicates that the change from mode TEM₀₀ to mode TEM_01* decreases the evaporation loss for all four calculations made. Thus, the laser profile corresponding to mode TEM_01* seems to provide more efficient laser power density distribution (Figure 10).

4. Discussion

It should be noted that the proposed dynamic model could not be used for precise data on the thermal history and simulation of the thermal stresses. The point was in researching an optimal laser power density distribution for the engineering tasks of LPBF. As known, the optimal melt pool configuration for the tasks of thick (more than 10 mm in thickness) material laser cutting or welding is torch-like (Figure 11) [25] and has a certain disadvantage when the laser power exceeds 100 W [26]. For laser scribing, surface treatment, and LPBF [40,41], the optimal one can be a more surface-like uniform distribution related to the following issues [60]:

• avoiding overheating in the centrum of the melt pool and consequences such as material loss on evaporation and ejecting granules from the melt pool of thermal heat with the laser power set at more than 100 W;
• avoiding secondary remelting and involvement of the previously solidified layers in the newly formed melt pool; and
• melt ejection under steam pressure.

The conducted research confirmed the effectiveness of the proposed approach not only for static modeling but for a dynamic one, as well. Achieved laser beam profiles are presented in Figure 12. As can be seen (Figure 12c), the flat-top profile is practically hard to be achieved close to the theoretical profile using the existed optical means [60]. The provided Figure 12d–f are reconstructed from the formed CoCr single tracks (Figure 12g–i) [61,62]. A detailed description of the developed LPBF setup equipped with an optical laser beam profiler and expander and optical diagnostics are presented in [26]. The experimental conditions are presented in [57]. Figure 13 presents the optical and modulation systems of LPBF setup.

The dynamic melt pool evaluation during experiments with metallic powders by optical diagnostic means [63,64] is expected for further research.

It should be noted that TEM_FT cannot be called a “desirable intensity distribution” since it was a theoretical proposal [50]. The idea was to achieve a more uniform energy density instead of peaks in the centrum of the laser beam spot. The picture of energy distribution in the laser beam spot and adsorbed energy by powder material is different. However, it can be even more varied, considering the dynamic factor (Pe number). Desirability can only be called a distribution that allows the achievement of uniform energy adsorption in the laser beam spot [57], taking into account the used material’s thermal conductivity and dynamic factor. Definitely, it will be already varied for metallic [65,66] and ceramic [67,68,69] groups of materials. However, it can also vary depending on granulomorphometric parameters of the powder, mainly shape and reflect ability [45,70,71], which was not considered in the article. The TEM₀₀ + TEM_01* equation is the only way to achieve approximate TEM_FT by existing optical means [72,73].

Comparing two radiation beams with different profiles is possible only with the different values for laser beam spot radii (Table 7). The same LPBF setup with a similar laser beam diameter provided technically and focused on a plane for all cases is practically used in the conditions of real production. Laser beam diameter corresponds to the main characteristics of the LPBF equipment (in our case, it is up to 100 µm) and cannot be changed quickly. The alternative laser beam profiles are experimentally achieved using a laser beam profiler and an expander and optically evaluated [60]. That was taken as a basis for theoretical evaluation of the dynamic factor to be closer to the common industrial conditions.

The average laser beam power distribution (E, J/m²) will not be similar in these cases as it was previously evaluated and compared (Table 5). Still, the question is not in the energy density in the laser beam spot radii, but in the practically achievable profile that can be useful and implemented in standard or experimental LPBF equipment (Figure 13).

Practically, the achievable profile by mixing TEM₀₀ and TEM_01* is far from the profile simulated based on Equation (2) due to the use available for market optical means. Moreover, as it was shown theoretically, the TEM_FT profile is not the one that corresponds the most to the technological tasks of LPBF of metallic powder with the high material thermal conductivity (λ).

5. Conclusions

Three radial laser beam profiles of the power density distribution (energy flux) were compared for laser powder bed fusion. The uniform cylindrical (flat-top) distribution (TEM_01* + TEM₀₀ mode) was compared with the standard Laguerre–Gaussian law distribution TEM₀₀ and the airy distribution of the first harmonic TEM_01* (TEM₀₁ + TEM₁₀ mode).

The TEM₀₀ laser beam profile demonstrated the most effective result for a wide range of temperatures for thermos-activated processes such as laser powder bed fusion in the Péclet number range of 0–2.86, while the uniform cylindrical (flat-top) distribution is shown to be effective in a narrow temperature range. The inverse Gaussian (donut) laser beam distribution showed an interval result. With an increase in laser power, the transition from TEM₀₀ to TEM_01* mode reduces the evaporation losses by more than 2.5 times, and it increases the absolute laser bandwidth when the relative bandwidth decreases by 24%.

The prospects of laser beam profiling for the purposes of increasing laser powder bed fusion productivity stay underestimated by the industry. However, they have a huge potential in the context of the switch to the sixth technological paradigm associated with Kondratieff’s waves.